Use of electrochemical impedance spectroscopy to determine double-layer capacitance in doped nonpolar liquids

Yezer, Benjamin A.; Khair, Aditya S.; Sides, Paul J.; Prieve, Dennis C.

doi:10.1016/j.jcis.2014.08.052

Cited by 54 publications

(56 citation statements)

References 31 publications

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“…Here, the permittivity ε and resistivity χ of each phase are measured via electrochemical impedance spectroscopy (Yezer et al 2014). The viscosity µ of each fluid is measured using a cone-and-plate rheometer (D-HR 2 rheometer, TA Instruments).…”

Section: Comparison Of Computation Against Experimentsmentioning

confidence: 99%

Nonlinear electrohydrodynamics of slightly deformed oblate drops

2015

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The transient deformation of a weakly conducting ('leaky dielectric') drop under a uniform DC electric field is computed via an axisymmetric boundary integral method, which accounts for surface charge convection and a finite relaxation time scale over which the drop interface charges. We focus on drops that attain an ultimate oblate (major axis normal to the applied field) steady-state configuration. The computations predict that as the time scale for interfacial charging increases, a shape transition from prolate deformation (major axis parallel to the applied field) to oblate deformation occurs at intermediate times due to the slow buildup of charge at the surface of the drop. Convection of surface charge towards the equator of the drop is shown to weaken the steady-state oblate deformation. Additionally, convection results in sharp shock-like variations in surface charge density near the equator of the drop. Our numerical results are then compared with an experimental system consisting of a millimetre-sized silicone oil drop suspended in castor oil. Agreement in the transient deformation is observed between our numerical results and experimental measurements for moderate electric field strengths. This suggests that both charge relaxation and charge convection are required, in general, to quantify the time-dependent deformation of leaky dielectric drops. Importantly, accurate prediction of the observed modest deformation requires a nonlinear model. Discrepancies between our numerical calculations and experimental results arise as the field strength is increased. We believe that this is due to the observed onset of rotation and three-dimensional flow at such high electric fields in the experiments, which an axisymmetric boundary integral formulation naturally cannot capture.

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Section: Comparison Of Computation Against Experimentsmentioning

confidence: 99%

Nonlinear electrohydrodynamics of slightly deformed oblate drops

2015

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“…An impedance is then defined as Z = V (t)/I(t) and will be a function of frequency only. The linearized PNP equations can be used to derive analytical formula for the impedance [24][25][26]. Expressed as a complex number, the real (in-phase) part of the impedance corresponds to the resistive nature of the electrolyte via its conductivity; the complex (out-ofphase) part corresponds to the capacitive nature of the Debye layers and the dielectric solvent.…”

Section: Introductionmentioning

confidence: 99%

“…Expressed as a complex number, the real (in-phase) part of the impedance corresponds to the resistive nature of the electrolyte via its conductivity; the complex (out-ofphase) part corresponds to the capacitive nature of the Debye layers and the dielectric solvent. At large voltages, V o > k B T /e, the diffuse charge dynamics are no longer linear; hence the current contains harmonic overtones and its amplitude is not linearly proportional to V o [25][26][27][28]. Thus, larges voltages are typically avoided when measuring impedance.…”

Section: Introductionmentioning

confidence: 99%

Moderately nonlinear diffuse-charge dynamics under an ac voltage

Stout

Khair

2015

Phys. Rev. E

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The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

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“…smaller

κ a

and thus larger

L (κ a)

) and larger ion size (smaller D ). A surfactant‐doped nonpolar liquid is such a material, for which

κ^{- 1}

can be on the order of hundreds of nanometers, and the charge carriers are inverted micelles of the surfactant .…”

Section: Lift Force On a Particle Undergoing Electrophoresis In Simplmentioning

confidence: 99%

The lift force on a charged sphere that translates and rotates in an electrolyte

Khair

Balu

2019

Electrophoresis

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The distortion of the charge cloud around a uniformly charged, dielectric, rigid sphere that translates and rotates in an unbounded binary, symmetric electrolyte at zero Reynolds number is examined. The zeta potential of the particle ζ is assumed small relative to the thermal voltage scale. It is assumed that the equilibrium structure of the cloud is slightly distorted, which requires that the Péclet numbers characterizing distortion due to particle translation, italicPet=Ua/D, and rotation, italicPer=Ωa2/D, are small compared to unity. Here, a is radius of the particle; D is the ionic diffusion coefficient; U=|U| and Ω=|boldΩ|, where U and Ω are the rectilinear and angular velocities of the particle, respectively. Perturbation expansions for small Pet and Per are employed to calculate the nonequilibrium structure of the cloud, whence the force and torque on the particle are determined. In particular, we predict that the sphere experiences a force orthogonal to its directions of translation and rotation. This “lift” force arises from the nonlinear distortion of the cloud under the combined actions of particle translation and rotation. The lift force is given by bold-italicF lift =Lfalse(κafalse)false(εa3ζ2/D2false)U×boldΩfalse[1+O(italicPet,italicPer)false]. Here, ε is the permittivity of the electrolyte; κ−1 is the Debye length; and L(κa) is a negative function that decreases in magnitude with increasing κa. The lift force implies that an unconstrained particle would follow a curved path; an electrokinetic analog of the inertial Magnus effect. Finally, the implication of the lift force on cross‐streamline migration of an electrophoretic particle in shear flow is discussed.

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Use of electrochemical impedance spectroscopy to determine double-layer capacitance in doped nonpolar liquids

Cited by 54 publications

References 31 publications

Nonlinear electrohydrodynamics of slightly deformed oblate drops

Nonlinear electrohydrodynamics of slightly deformed oblate drops

Moderately nonlinear diffuse-charge dynamics under an ac voltage

The lift force on a charged sphere that translates and rotates in an electrolyte

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