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A system enabling electrically actuated, time-lapse epi-MISS imaging was developed around an inverted microscope platform (Fig. 1). The system combines a novel MISS set-up34 in reflection (epi) mode (Fig. 1a), an optoelectrochemical cell comprising counter, reference, and working electrodes (CE, RE, and WE), and an electrical AC signal generator (Fig. 1b). This new system yields with high spatial resolution the following quantities: (1) the quantitative phase map (epi-MISS) via the DC component of the electrically actuated time-lapse MISS images and (2) the electrical impedance map of the sample via the distribution of the phase-amplitude oscillation at the frequency of the AC electric field (el-epi-MISS).
Fig. 1 Schematics of the measurement system.
a The epi-MISS optical set-up based on an inverted microscope, a grating and magnified image spatial spectrum based on a 4-f system with a gradient-index, GRIN, lens (f1 = 60 mm, f2 = 150 mm, f3 = 0.3 mm; L3 and L2 form a 4-f system that magnifies the Fourier transform of the zero-order by a factor of 500); b Schematic representation of an optoelectrochemical cell with CE, RE, and WE and of the measuring principle -
A dedicated calibration chip was fabricated to validate the capability of the proposed optoelectrochemical method (Fig. 2). This chip was designed to carry nanometer-sized, disk-shaped areas with optical and electrical properties that are different from those of the background. The chip is integrated as the WE in an electrochemical cell (Fig. 1b) configured with a transparent dielectric coating. The chip, fabricated via sequential deposition, comprises a continuous indium tin oxide (ITO) layer and a perforated titanium dioxide (TiO2) upper layer with ~550 nm diameter holes exposing the underneath ITO layer. Note that the TiO2 layer has a higher reflectivity than the ITO-exposed surfaces. In terms of electrical contrast, both materials are semiconductors, and their different interfacial electrical properties are expected to provide a contrast that is dependent on the frequency of the applied electrical modulation. Importantly, to highlight the sensitivity of our technique, we constructed the calibration chip to display areas with rather subtle differences in terms of electrical properties; both ITO and TiO2 are semiconductors, rather than coarse electrical contrast between, for instance, a dielectric vs. a conductor. For example, a calibration chip featuring only nanostructured, perforated TiO2 deposited directly onto glass will have displayed areas with drastic differences in terms of electrical properties. In our set-up, the dielectric reference is offered by the transparent polymer over-layer used to configure the electrochemical cell.
Fig. 2 Schematic representation of the nanopatterned calibration chip fabrication steps.
The different electrical (relative permittivity, εi) and optical (reflectance, Ri) properties of the two materials, i = TiO2 and ITO, tailor the optical and electrical contrast of the chip that is included in an electrochemical cell using a dielectric flow cell boundary -
As shown in Fig. 3a, each frame acquired over a rectangular area of the chip represents an interferogram that allows the reconstruction of a quantitative phase map Φ(x, y) via a Hilbert transform method36. A heightmap can be further estimated based on the individual pixel quantitative phase information (Fig. 3b), according to:
Fig. 3 Data processing workflow.
a Acquired raw images (interferograms) at distinct time points. b Reconstructed phase maps (epi-MISS images) at distinct time points. c 2D phase map averaged over 176 frames (epi-MISS). d Time series of the phase variation (for one point in the field of view) upon AC electrical actuation at 0.5 Hz (black) and without AC (red); the actuation signal is depicted in green. e Frequency spectra derived from individual pixels time series in (d). f 2D map of the optical phase modulation amplitude, δΦ(ωAC, x, y), derived from the bandpassing signal at approximately 0.5 Hz (el-epi-MISS); the dotted yellow line indicates the polydimethylsiloxane (PDMS) layer delimiting the electrochemical cell; due to its transparency and isolator nature, the PDMS layer is only visible in the map with electrical contrast$$ {\mathrm{h}}(x, y) = \frac{{\Phi \left( {x, y} \right) \cdot \lambda _0}}{{2 \cdot 2{\pi} \cdot \Delta n}} $$ (1) where h(x, y) and Φ(x, y) are the height and optical phase profiles, respectively, Δn is the refractive index difference (1.33 for our conditions), and λ0 is the wavelength of the incident light in a vacuum (532 nm for the laser used in our experiments). In reflection, the light travels to the interface and back, requiring an additional factor of 2 in the denominator of Eq. (1) to account for the double pass. The time average over the image sequence Φ(x, y, t) provides the topography of the sample (Fig. 3c).
The dependence of the measured optical phase values, Φ(x, y, t), on the applied AC electric field (Fig. 3d) was demodulated using a discrete Fourier transform (DFT). From the resulting temporal power spectrum bandpassed around the modulation frequency, we precisely extracted the amplitude δΦ(ω, xi, yi) of the optical phase modulation as a function of the applied AC electrical signal (Fig. 3e) at every pixel (xi, yi) in the QPI image. The resulting map δΦ(ωAC, x, y) provides the el-epi-MISS image of interest at the frequency of the AC external electric voltage (Fig. 3f). To minimize the DFT calculation errors, we analyzed the time series over intervals that correspond to an integer number of periods (inverse of the applied AC frequency).
Figure 3c, f illustrates the capability of the proposed approach to reveal both optical and electrical impedance contrast. El-epi-MISS imaging offers a quantitative way to reveal the electrical heterogeneity and contrast of the electrified interfaces, complementing the topographic information. Note that the dielectric over-layer (in green in Fig. 2) is visible only in the el-epi-MISS image (Fig. 3f). Furthermore, high spatial resolution impedance contrast is evident in the area not covered with a dielectric overlay, with distinct spots of higher impedance appearing darker than the surrounding lower impedance regions.
To enable a comparison with the topography map (in Fig. 3c and Supplementary materials, Fig. S3), we expressed the el-epi-MISS image in terms of both the optical phase modulation amplitude δΦ(ωAC, x, y), which is the actual representation of the electric field modulation according to the Theoretical Section (see Fig. 3f) and the equivalent height modulation $\delta h(x, y) = \frac{{\delta \Phi \left( {\omega _{AC}, x, y} \right) \cdot \lambda _0}}{{2 \cdot 2\pi \cdot \Delta n}}$, presented in Supplementary materials, Fig. S3b.
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The holes in the TiO2 over-layer are clearly visible in the epi-MISS images (Fig. 3b). While this phase contrast is due to the lower reflectivity of the TiO2-free regions, the quantitative feature of epi-MISS maps (Fig. 3c) provides a clear estimation of the TiO2 layer thickness. Our results indicate an average thickness of ~50 ± 5 nm, which is close to the value targeted by our fabrication design. Figure S3 in the Supplementary materials provides a thorough comparison between these optical measurements and those derived from AFM data.
We validated our spatial resolution by comparing the diameters of the TiO2 holes measured by epi-MISS with those measured by AFM. We obtained 470 ± 70 nm, which compares well with the AFM results, of 551 ± 42 nm, as shown in Fig. S3 of the Supplementary materials.
Having a common path geometry19, epi-MISS, and el-epi-MISS are characterized by low temporal path-length noise. The temporal noise of el-epi-MISS is given by the standard deviation of the DFT phase-amplitude at the electrical actuation frequency for each pixel and is ~ 0.3 ± 0.1° (Supplementary materials), yielding an SNR of ~30 dB for the electroactive area ($SNR = 10{\mathrm{Log}}[10, ({{S}}/{{N}})^2]$). Notably, a similar noise level of ~0.3° is obtained without electrical modulation.
To prove that the el-epi-MISS images (Fig. 3f) effectively reveal the electrical impedance distribution of the structured interface, we used the frequency modulation of the electrical actuation of the el-epi-MISS data in a matching domain with classic EIS measurements of the macro-electrodes.
The dependence of the optical phase oscillation amplitude on the electrical field modulation is described in the Methods section (see "Theoretical model"). This theoretical model allows us to extract the magnitude of the electrical impedance, Zt (ωAC, x, y), as a function of the measured δΦ(ωAC, x, y), namely:
$$ Z_t\left( {\omega _{AC}, x, y} \right) \approx \frac{{\alpha _{phase}}}{{S \cdot \omega _{AC}}} \cdot \frac{{\delta V_{AC}}}{{\delta \Phi \left( {\omega _{AC}, x, y} \right)}} $$ (2) where αphase is a constant (C-1 m-1), dependent on the electrode chip structure, S is the electrode surface, ωAC is the angular frequency for the AC field, and δVAC is the magnitude of the applied electric potential.
El-epi-MISS images were acquired over the same chip area with δVAC kept at the same value of 0.58 V and varying the AC field frequencies between 0.2 Hz and 1.6 Hz. The amplitude of the optical phase variation as a function of the applied AC electrical signal representative of ITO and TiO2 materials was derived from averaging specific areas over 3 × 3 pixels (i.e., 104 nm2), corresponding to the ITO and TiO2 regions (i.e., inside and outside holes). According to Fig. 4a, the amplitude of the phase variation as a function of the applied AC electrical signal reveals quantitative differences between the two materials, indicative of different impedances over the entire applied frequency range.
Fig. 4 Surface electrical contrasts.
a The amplitude of the optical phase modulation averaged for multiple specific areas on the surfaces corresponding to holes and the TiO2 coating vs. the electrical actuation frequency. b Average TiO2 impedance measured by both EIS and el-epi-MISS (Zt(ωAC, x, y))To quantitatively compare the frequency-dependent el-epi-MISS-derived data to the conventional EIS data (Fig. 4b), the macroscopic impedance of the same TiO2-coated electrode was measured by EIS between 0.2 and 1.6 Hz. The modulus of the macroscopic impedance (Z) was compared to the el-epi-MISS-derived TiO2 impedance since more than 70% of the exposed surface is TiO2. Figure 4b shows a good match between the impedance module values derived by the conventional EIS assay and el-epi-MISS. Moreover, as revealed by Fig. 4b, based on Eq. (2), we experimentally derived the value of the linear coefficient αphase ~17 C-1 m-1 (S~1 mm2, δVAC = 0.58 V).
Based on Eq. (2), an impedance map of the nanopatterned surface is derived (Fig. 5a), and the profiles corresponding to holes in the TiO2 layer an ~500 nm diameter (Fig. 5b), irrespective of the analyzed frequency (Fig. 5c). A thorough analysis of the hole diameters in el-epi-MISS images (see Supplementary materials Fig. S3b) highlights a 513 ± 48 nm average diameter, which compares well with the diameter revealed by AFM measurements (551 ± 42 nm).
Fig. 5 Submicrometric spatial resolution with high electric contrast obtained by el-epi-MISS measurements.
a El-epi-MISS impedance map at 0.5 Hz. b Profile corresponding to the yellow line and indicating a generic, individual hole in the TiO2 layer. c The same profile corresponding to an individual hole in the TiO2 layer at 1.6 Hz
Development of a novel set-up enabling epi-MISS and el-epi-MISS
Development of a calibration chip providing electrical and optical contrast at the nanoscale
Optimized protocol to derive 2D maps with topographical (phase) and electrical contrasts
El-epi-MISS figures of merit
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In MISS microscopy, the reference field for QPI is generated using a GRIN lens (350 µm diameter, an effective focal length of 300 µm) to magnify the Fourier transform of the zero-order to the point where the DC component fills the camera sensor34. MISS is characterized by low spatiotemporal path-length noise (0.6 nm temporal noise and 2.8 nm spatial noise floor)36. Due to the more efficient collection of the reference order and highly stable low noise statistics, MISS is ideal for high-throughput QPI investigations, such as dynamic light scattering and cellular membrane mechanics34 assays.
The light emitted by the laser diode laser (LMX-532L-100-COL-PP, Oxxius, France) at 532 nm was fiber-coupled, collimated, and used as an epi-illumination source for an inverted microscope (Axio Observer Z1, Zeiss, Oberkochen, Germany). All imaging was carried out using a 100× oil immersion objective (1.46 NA, WD = 0.11 mm). The nanostructured slide was illuminated from the bottom, and the reflection image plane exiting the microscope was relayed to an EMCCD camera (iXonEM + 885, Andor, Belfast, UK) using a 4f system based on lenses L1 and L2 (Fig. 1a). A diffraction grating (Edmund Optics, New Jersey, USA; 110 lp/mm) was placed precisely at the image plane outside the microscope to separate the image field into multiple orders, each containing complete information about the object. At the Fourier plane of L1, the zeroth diffraction order was passed through a GRIN lens L3 (Edmund Optics), while the first diffraction order passed through unaffected. In combination with L2, lens L3 formed a 4f system that produces a highly magnified image of the zeroth-order Fourier spectrum at the camera plane34.
For the el-epi-MISS measurements, the time series of variable length (between 200 and 400 frames) of the reflectivity interferograms of magnified images of actuated nanostructured surfaces were acquired at up to 21.3 frames per second when driven by sinusoidal fields with frequencies between 0.2 and 1.6 Hz (0.2, 0.4, 0.5, 0.8, 1.6 Hz). The system was actuated by applying a signal of 0.58 V, suitable to drive stable oscillations of the optical intensity.
When illuminated with laser light and imaged in the reflection mode using the set-up in Fig. 1, each interferogram was processed based on the spatial Fourier transform36 to reconstruct the phase map of the optical contrast of the chip structure.
The dependence of the phase map Φ(x, y) on the applied electric actuation (VAC amplitude and frequency) for each pixel was reflected in the time series of the quantitative phase images Φ(t, x, y) that were analyzed by a DFT performed on each pixel of the phase map Φ(x, y) in the time domain.
The resulting map of the amplitude of the oscillatory response of the quantitative phase values δΦ(ωAC, x, y) upon actuation, derived from DFT at the applied frequency, provides the el-epi-MISS image.
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An impedance analyzer (Solartron 1260, Hampshire, UK) and a potentiostat (CellTest 1470E, Solartron) were used to impose AC actuation over the microfluidic electrochemical cell assessed using both el-epi-MISS and conventional EIS measurements. The electrochemical cell consists of a three-electrode system: miniaturized Ag/AgCl, 3M KCl, (World Precision Instruments, Florida, USA) as the RE, Pt wire as the CE, and the nanopatterned surface as the WE, exposed to the electrolyte in a PDMS gasket (Fig. 1b).
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Figure 2 presents the fabrication steps of the nanopatterned chips. First, an ITO layer was deposited on a glass substrate by physical vapor deposition. Then, nanopatterning was achieved via colloidal lithography. This operation requires the self-assembly of close-packed polystyrene (PS) spheres 980 nm in diameter on the ITO substrate. The PS spheres were further etched with reactive ion etching to the desired size, representing the final diameter (~550 nm). Subsequently, TiO2 was deposited on the PS-decorated ITO surface. The nanopatterned chip was obtained by lift-off of the PS spheres with adhesive tape, followed by a cleaning step. The detailed protocol is presented in the Supplementary materials.
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All electrical measurements were performed in a phosphate-buffered saline solution (pH 7.4) containing 137 mM NaCl, 10 mM phosphate, and 2.7 mM KCl as the running buffer. Ultrapure water (Merck Millipore, Guyancourt, France) was used throughout the preparations. All chemical reagents were purchased from Sigma Aldrich (Missouri, USA), were of analytical grade, and were used without further purification.
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This section and the Supplementary materials substantiate the background to measure the electric field locally with an optical phase method.
The physical and chemical phenomena that occur when an electric field is applied at the electrode-liquid interface have been extensively discussed in the literature43, 44.
Different mechanisms take place at this interface and can be responsible for altering the refractive index of the interface and the optical phase values, namely, the changes in the Helmholtz double-layer, electronic density, and oxidation of the electrode film. These phenomena depend on both the electrode material and the solution in contact with the electrode as well as on the amplitude of the applied potential. According to Gouy-Chapman theory, the surface charge density at the electrode-electrolyte interface for symmetric electrolyte is equal to45:
$$ \sigma = \left( {8kT \cdot \varepsilon _l\varepsilon _0 \cdot n} \right)^{1/2}\sinh \frac{{z \cdot e \cdot \left( {\phi _0 - \phi _s} \right)}}{{2kT}} $$ (3) where k is the Boltzmann constant, T is the absolute temperature, εl is the dielectric constant of the electrolyte solution, ε0 is the permittivity of vacuum, n is the bulk concentration of charges, z is the valence of the electrolyte, e is the elementary electric charge, ϕ0 is the electrostatic potential at the electrode-electrolyte interface, and ϕs is the electrostatic potential at the outer Helmholtz layer.
Based on the Drude-Lorentz model46-48, one can derive the dependence of the components of the dielectric constant of the thin layer εtl of the solid facing the electrolyte (with the thickness equal to the penetration depth of the quasi-static electromagnetic field) on the surface charge distribution, as well as the related variations due to an AC electric field49:
$$ \delta \varepsilon ^{\prime}_{tl}\left( {\omega _{AC}, x, y} \right) = - \left( {\varepsilon ^{\prime}_{tl} - 1} \right) \cdot \frac{{\delta \sigma \left( {\omega _{AC}, x, y} \right)}}{{n_e \cdot e \cdot d_{tl}}}\\\delta \varepsilon ^{\prime\prime}_{tl}\left( {\omega _{AC}, x, y} \right) = \varepsilon ^{\prime\prime}_{tl}\frac{{\delta \sigma \left( {\omega _{AC}, x, y} \right)}}{{n_e \cdot e \cdot d_{tl}}} $$ (4) where dtl is the penetration depth of the electric field (the Thomas-Fermi screening length) within the electrode at the electrode-liquid interface, εtl ($\varepsilon _{tl} = \varepsilon ^{\prime}_{tl} + j\varepsilon ^{\prime\prime}_{tl}$) is the free-electron contribution to the dielectric constant of the electrode, and ne is the free-electron density of the bulk solid. Corresponding to the same material, εtl differs from εel due to the biasing effect of the DC value of the electrode potential, which is additionally modulated by the local AC field.
According to equations (s1) and (s2) in the Supplementary materials, the AC electrically modulated surface charge distribution at the electrode-liquid interface is:
$$ \delta \sigma \left( {\omega _{AC}, x, y} \right) \approx - \varepsilon _l\varepsilon _0\delta \frac{{\partial \mathop {\phi }\nolimits_l \left( {\omega _{AC}, x, y, z \to {\mathrm{0}}} \right)}}{{\partial \;{\mathrm{z}}}} $$ (5) where ϕl(ωAC, x, y, z→0) is the local AC electric potential in liquid at the electrode-liquid interface and εl is the relative permittivity of the liquid.
Since our assay involves non-faradaic currents13, 50 (low applied potentials), the variation in the surface charge density is related to sample impedance (for derivation, see equations (s3)-(s5)) via:
$$ \delta \sigma \left( {\omega _{AC}, x, y} \right) = \frac{{\delta V_{AC}}}{{\omega _{AC} \cdot S \cdot Z_t\left( {\omega _{AC}, x, y} \right)}} $$ (6) Consequently, one obtains:
$$\begin{array}{l}\delta \varepsilon ^{\prime}_{tl}\left( {\omega _{AC}, x, y}\, \, \, \right) = - \frac{{\left( {\varepsilon ^{\prime}_{tl} - 1} \right)}}{{e \cdot n_e \cdot d_{tl}}} \cdot \frac{{\delta V_{AC}}}{{\omega _{AC} \cdot S \cdot Z_t\left( {\omega _{AC}, x, y} \right)}}\\\delta \varepsilon ^{\prime\prime}_{tl}\left( {\omega _{AC}, x, y} \right)\ = \frac{{\varepsilon ^{\prime\prime}_{tl}}}{{e \cdot n_e \cdot d_{tl}}} \cdot \frac{{\delta V_{AC}}}{{\omega _{AC} \cdot S \cdot Z_t\left( {\omega _{AC}, x, y} \right)}}\end{array} $$ (7) To relate the electrical structure of the sample to the 2D phase map when applying an AC electric field in an epi-MISS set-up, one has to connect the impedance formalism above to the multilayered sensing chip in the context of the general formalism based on Fresnel equations to derive the 2D distribution of the phase amplitudes as a function of the electrical impedance fingerprint of the sample and the parameters of the chip (as illustrated in Fig. 6).
Fig. 6 Schematic representation of the equivalent electrical circuit.
Phase variation is linearly dependent on the relative permittivity shift, driven by the (local) electric field, of the liquid-sensor interfaceIndeed, based on Fresnel equations, we derive the variation in the phase difference between the incident and reflected light (Φ(x, y) in equation (s7), Supplementary materials), modulated by the electrically active upper-most interface, also dependent on the structure of the sensing chip (εi, di):
$$ \delta \Phi \left( {\omega _{AC}, x, y} \right) = \delta \Phi \left[ {\delta \varepsilon _{tl}, Z_t\left( {\omega _{AC}, x, y} \right), \varepsilon _i, d_i} \right] $$ (8) The phase variation is linearly dependent (in a first approximation), via Kphase, on the relative permittivity shift, δεtl driven by the (local) electric field, of the liquid-sensor interface. For a given structure of the sensing chip (with known parameters εi and di), the variation in the phase magnitude relates to δεtl via:
$$ \delta \Phi \left( {\omega _{AC}, x, y} \right) \approx K_{phase}\delta \varepsilon _{tl}\left( {\omega _{AC}, x, y} \right) $$ (9) Consequently, since the highest impact is given by ε′tl,
$$ \delta \Phi \left( {\omega _{AC}, x, y} \right) \approx K_{phase} \cdot \frac{{\left( {\varepsilon^{\prime}_{tl} - 1} \right)}}{{e \cdot n_e \cdot d_{tl}}}\frac{{\delta V_{AC}}}{{S \cdot \omega _{AC}}}\frac{1}{{Z_t\left( {\omega _{AC}, x, y} \right)}} $$ (10) By denoting αphase as:
$$ \alpha _{phase} = K_{phase} \cdot \frac{{\left( {\varepsilon^{\prime}_{tl} - 1} \right)}}{{e \cdot n_e \cdot d_{tl}}} $$ (11) one obtains the dependence of the variation in the optical phase-amplitude on the magnitude of the electrical impedance of the sample (similar to Eq. (2)):
$$\delta \Phi \left( {\omega _{AC}, x, y} \right) \approx \alpha _{phase}\frac{{\delta V_{AC}}}{{S \cdot \omega _{AC}}}\frac{1}{{Z_t\left( {\omega _{AC}, x, y} \right)}} $$ (12) Combining Eqs. (6) and (11), one relates the phase to the AC variation of the surface charge density:
$$ \delta \Phi \left( {\omega _{AC}, x, y} \right) \approx \alpha _{phase}\delta \sigma \left( {\omega _{AC}, x, y} \right) $$ (13) Both the theoretical simulations and the experimental results reveal a quasi-linear dependency of the phase-amplitude, δΦ, on the excitation, with δVAC yielding a similar value of the linear coefficient αphase, ~17 C-1 m-1.
Notably, the simulation reveals that the ratio Kphase/dtl does not depend on dtl in the range of 1 nm ÷ 0.1 nm; therefore, assuming the precise value of the Thomas-Fermi screening length is not critical for deriving αphase.
The relations in Eq. (7) encompass the core of the electro-optical phenomena concerning non-faradaic approaches. They generically relate the modulation of the dielectric constant of the thin layer of the electrode facing the electrolyte to the sample impedance and the parameters of the applied electric field. As a limiting factor of this cause-effect relation, the frequency of the AC field at the denominator restricts the applicability of electro-optical assays to frequencies below ~100 kHz, even though cameras with megahertz frame rates became available42.
Moreover, Eqs. (12) and (13) apply to other electro-optical methods, e.g., involving plasmonics13, 41, with particular values for the respective linear coefficient.