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6CCVD Research

Sensing Electrochemical Signals Using a Nitrogen-Vacancy Center in Diamond

At a Glance

Section titled ā€œAt a Glanceā€
MetadataDetails
Publication Date2021-02-01
JournalNanomaterials
AuthorsHossein T. Dinani, Enrique MuƱoz, Jeronimo R. Maze
InstitutionsUniversidad Mayor, Pontificia Universidad CatĆ³lica de Chile
Citations5
AnalysisFull AI Review Included

Executive Summary

Section titled ā€œExecutive Summaryā€

This theoretical work proposes using the Nitrogen-Vacancy (NV) center in bulk diamond as a highly sensitive nanosensor to estimate ion concentration (cb) in an electrolyte solution (e.g., Cu2+/SO42-) by monitoring its electron spin decoherence.

  • Core Value Proposition: The diffusional fluctuations of ions in the electrolyte generate electric field noise, which directly increases the inhomogeneous dephasing rate (1/T2*) of the NV electron spin.
  • High Concentration Sensing (cb > 0.04 mol/m3): The induced dephasing rate (1/T2) is the primary signal. For cb > 100 mol/m3, the induced 1/T2 exceeds 300 kHz, significantly competing with the intrinsic NV dephasing rate.
  • Scaling Law: The induced dephasing rate follows a power law relationship with bulk concentration: 1/T2* ~ A * cbB, where B ā‰ˆ 0.417.
  • Low Concentration Sensing (cb < 0.1 mol/m3): The static electric field gradient (Stark effect) at the NV position becomes the dominant sensing mechanism, providing a measurable energy shift (39 kHz shift for a one order of magnitude change in cb).
  • Sensitivity: At cb = 10 mol/m3, the calculated sensitivity is 3.27 mol m-3 Hz-1/2, achievable via Free Induction Decay (FID) measurements.
  • Material Advantages: Diamond provides a bio-compatible, resilient platform suitable for miniaturization and operation under extreme chemical conditions.

Technical Specifications

Section titled ā€œTechnical Specificationsā€
ParameterValueUnitContext
NV Center Depth (d)10nmPosition of the NV center below the diamond surface (z=0).
Bulk Concentration (cb) Threshold (Dephasing)0.04mol/m3Minimum concentration for induced 1/T2* > 10 kHz.
Induced Dephasing Rate (High cb)> 300kHzAchieved at cb > 100 mol/m3.
Dephasing Rate Scaling (Exponent B)0.417unitlessPower law exponent in 1/T2* ~ cbB.
Dephasing Rate Scaling (Coefficient A)39,295Hz (mol/m3)-BFit coefficient for the numerical simulations.
Sensitivity (Ī·) (at cb = 10 mol/m3)3.27mol m-3 Hz-1/2Calculated using an evolution time (Ļ„) of 10 Āµs.
Electric Field Change (Low cb)230kV/mChange in ENV resulting from a one order of magnitude change in cb (for cb < 0.1 mol/m3).
Energy Shift (Low cb)39kHzEnergy shift corresponding to the 230 kV/m electric field change (at Ļ†Ī² = 0).
NV Zero Field Splitting (D)2.87GHzGround state spin triplet splitting.
Electron Gyromagnetic Ratio (Ī³e)2.8MHz/GUsed in the Hamiltonian calculation.
Diamond Dielectric Constant (Īµd)5.8Īµ0unitlessRelative permittivity of diamond.
Substitutional Nitrogen Density (Ds)1012cm-2Areal density of implanted nitrogens.
Diffusion Constant (D)2.3 x 10-9m2/sDiffusion constant used for Cu2+ and SO42- ions.
Temperature (T)298KStandard operating temperature for simulations.

Key Methodologies

Section titled ā€œKey Methodologiesā€

This work is based on a theoretical model combining electrochemical transport and quantum spin dynamics.

  1. Electrolyte Transport Modeling:

    • The steady-state concentration profiles and electric potential (Ļ†) inside the electrolyte (Cu2+/SO42-) were determined by solving the coupled non-linear Nernst-Planck (ion flux) and Poisson equations.
    • The electric potential was derived analytically, yielding the inverse screening length (Īŗ) and the equilibrium electric field (Eeq) at the diamond interface.

  2. Electric Field Fluctuation Derivation:

    • Thermal noise leads to small fluctuations in ion concentration (Ī“cs) around the equilibrium value.
    • The correlation function for these concentration fluctuations was derived using the Greenā€™s function solution to the diffusion equation, assuming a one-dimensional gradient (z-direction).
    • These concentration fluctuations were linked to electric field fluctuations (Ī“E) via the Poisson equation.

  3. Diamond and NV Center Electrostatics:

    • The electric potential (Ļ†) and electric field (E) inside the bulk diamond were calculated by solving the Poisson equation, incorporating the charge density (Ļd) from ionized substitutional nitrogen (Ns) and NV defects (NV-, NV+).
    • Boundary conditions (continuity of potential and displacement) were enforced at the electrolyte/diamond interface (z=0).

  4. Dephasing Rate Calculation (1/T2*):

    • The NV electron spin Hamiltonian (H) was used, including the zero-field splitting (D) and the electric field terms (HE0, HE1, HE2).
    • The fluctuations in the energy splitting (Ī“Ī½) due to electric field noise (Ī“ENV) were calculated.
    • The inhomogeneous dephasing rate (1/T2) was derived from the accumulated phase variance (āŒ©Ī“Ļ†2āŒŖ) in the Free Induction Decay (FID) signal, where 1/(T2)2 scales with āŒ©Ī“Ļ†2āŒŖ/Ļ„2.

  5. Ramsey Spectroscopy for Static Field Sensing:

    • For low concentrations (cb < 0.1 mol/m3), the static electric field gradient (ENV) is large enough to be measured via the Stark effect.
    • The NV spin is prepared in a superposition state (superposition of |0āŒŖ and |Ā±1āŒŖ states) using a perpendicular magnetic field, and the resulting energy shift is measured via a Ramsey sequence.

Commercial Applications

Section titled ā€œCommercial Applicationsā€

This NV-based electrochemical sensing technology is highly relevant for applications requiring robust, miniaturized, and highly sensitive concentration monitoring in liquid environments.

IndustryApplication/ProductTechnical Advantage
Chemical ProcessingProcess control in industrial electrolysis (e.g., copper electro-refining).High-precision monitoring of specific ion concentrations (e.g., Cu2+, SO42-) to ensure product purity.
Environmental MonitoringDetection and quantification of pollutant levels in water and industrial effluents.High sensitivity (down to 0.04 mol/m3 range) and resilience of the diamond sensor material.
Pharmaceutical/FoodAccurate measurement and control of ionic concentrations and pH levels.NV charge state and dephasing rate can be used for pH sensing (H+ concentration).
Fundamental Chemistry/BiologyIn situ monitoring of ion-channel function in cell membranes.Nanoscale spatial resolution and real-time measurement capability using quantum decoherence.
Miniaturized SensingDevelopment of robust, miniaturized electrochemical sensors for extreme conditions (high temperature, corrosive media).Diamondā€™s inherent bio-compatibility and resilience to harsh chemical environments.
View Original Abstract

Chemical sensors with high sensitivity that can be used under extreme conditions and can be miniaturized are of high interest in science and industry. The nitrogen-vacancy (NV) center in diamond is an ideal candidate as a nanosensor due to the long coherence time of its electron spin and its optical accessibility. In this theoretical work, we propose the use of an NV center to detect electrochemical signals emerging from an electrolyte solution, thus obtaining a concentration sensor. For this purpose, we propose the use of the inhomogeneous dephasing rate of the electron spin of the NV center (1/T2ā˜…) as a signal. We show that for a range of mean ionic concentrations in the bulk of the electrolyte solution, the electric field fluctuations produced by the diffusional fluctuations in the local concentration of ions result in dephasing rates that can be inferred from free induction decay measurements. Moreover, we show that for a range of concentrations, the electric field generated at the position of the NV center can be used to estimate the concentration of ions.

Tech Support

Section titled ā€œTech Supportā€

Original Source

Section titled ā€œOriginal Sourceā€

References

Section titled ā€œReferencesā€
  1. 2009 - Review on carbon-derived, solid-state, micro and nano sensors for electrochemical sensing applications [Crossref]
  2. 2014 - Nitrogen-Vacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology [Crossref]
  3. 2017 - Probing photoinduced electron-transfer in graphene-dye hybrid materials for DSSC [Crossref]
  4. 2019 - A film-forming graphene/diketopyrrolopyrrole covalent hybrid with far-red optical features: Evidence of photo-stability [Crossref]
  5. 2013 - The nitrogen-vacancy color center in diamond [Crossref]
  6. 2014 - Electronic Properties and Metrology Applications of the Diamond NVāˆ’ Center under Pressure [Crossref]
  7. 2013 - Nanometre-scale thermometry in a living cell [Crossref]
  8. 2011 - Electric-field sensing using single diamond spins [Crossref]
  9. 2014 - Magnetometry with nitrogen-vacancy defects in diamond [Crossref]
  10. 2008 - Nanoscale magnetic sensing with an individual electronic spin in diamond [Crossref]

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