Interdigitated electrodes
The interdigitated electrodes produce certain electric fields when voltage is applied, for capacitive measurements. The interdigitated electrodes provide greater effective surface area within the same volume or space which would drastically reduce the sensing setup and cost as compared to other capacitive measurement systems [28,29,30,31]. The electric field produced by the interdigitated electrodes is within the nanoscale range, which falls in the region of interest as the size of the antigens and antibodies lies in this range [32, 34]. The dielectric properties of the medium between the interdigitated electrodes provide the electrical information such as conductivity, permittivity, capacitance and impedance. The electric field lines produced by the interdigitated electrodes depend on the electrical input, dielectric medium, and the geometry of the electrodes.
The effective surface area of the electrode that contributes to the capacitance is, ‘Top’ surface area and ‘Side’ surface area as shown in Fig. 4a. The net capacitance ‘C’ of the active surface area (Top + Side) of the electrodes in the comprised capacitance model can be determined by Eq. (1),
$${\text{C}} = \upvarepsilon_{{{\text{r}}_{\text{T }} }} \cdot \upvarepsilon {\text{o}} \cdot \left( {\frac{{{\text{A}}_{{{\text{eff}}_{\text{Top}} }} }}{{{\text{d}}_{{{\text{eff}}_{\text{Top}} }} }}} \right) + \upvarepsilon_{{{\text{r}}_{\text{S }} }} \cdot \upvarepsilon {\text{o}} \cdot \left( {\frac{{{\text{A}}_{{{\text{eff}}_{\text{Side}} }} }}{{{\text{d}}_{{{\text{eff}}_{\text{Side}} }} }}} \right)$$
(1)
where \(\upvarepsilon_{{{\text{r}}_{\text{T }} }}\) and \(\upvarepsilon_{{{\text{r}}_{\text{S }} }}\) is the relative permittivity of the material on the top and side surfaces of the electrode, \(\upvarepsilon {\text{o}}\) is the vacuum permittivity, \({\text{A}}_{{{\text{eff}}_{\text{Top}} }}\) and \({\text{A}}_{{{\text{eff}}_{\text{Side}} }}\) are the effective surface areas on the top and side surfaces of the electrode, and \({\text{d}}_{{{\text{eff}}_{{_{\text{Top}} }} }}\) is the effective distances neighboring two top surfaces and \({\text{d}}_{{{\text{eff}}_{{_{\text{Side}} }} }}\) is between the adjacent two side surfaces of the electrode.
When the SAM, Antibody and Antigen/Antibody layers are assumed to be homogenous over the surface of electrode, the capacitance of the circuit can be calculated from the equivalent model, with the single surface (Top + Side) as shown in Fig. 4b.
Hence, the net capacitance ‘C’ of the approximately simplified model can be calculated as per Eq. (2),
$${\text{C}} = \upvarepsilon_{\text{r}} \cdot \upvarepsilon {\text{o}} \cdot \left( {\frac{{{\text{A}}_{\text{eff}} }}{{{\text{d}}_{\text{eff}} }}} \right)$$
(2)
And,
$${\text{C}} = {\text{C}}_{\text{Top}} {\text{ + C}}_{\text{Side}}$$
(3)
where,
$${\text{C}}_{\text{Top}} = \upvarepsilon_{{{\text{r}}_{\text{T }} }} \cdot \upvarepsilon {\text{o}} \cdot \left( {\frac{{{\text{A}}_{\text{Top}} }}{{{\text{d}}_{\text{Top}} }}} \right)$$
(4)
$${\text{C}}_{\text{Side}} = \upvarepsilon_{{{\text{r}}_{\text{S }} }} \cdot \upvarepsilon {\text{o}} \cdot \left( {\frac{{{\text{A}}_{\text{Side}} }}{{{\text{d}}_{\text{Side}} }}} \right)$$
(5)
By assuming,
$$\upvarepsilon_{{{\text{r}}_{ \, } }} \approx \upvarepsilon_{{{\text{r}}_{\text{T }} }} \approx \upvarepsilon_{{{\text{r}}_{\text{S }} }}$$
(6)
$${\text{A}}_{\text{eff}} \approx {\text{A}}_{{{\text{eff}}_{{_{\text{Side}} }} }} + {\text{A}}_{{{\text{eff}}_{{_{\text{Top}} }} }}$$
(7)
With Eq. (2) to Eq. (7) deff can be written as,
$${\text{d}}_{\text{eff}} \approx \frac{{{\text{A}}_{{{\text{eff}}_{{_{\text{Side}} }} }} + {\text{A}}_{{{\text{eff}}_{{_{\text{Top}} }} }} }}{{\left( {\frac{{{\text{A}}_{\text{eff}} }}{{{\text{d}}_{\text{eff}} }}} \right)_{\text{Side}} + \left( {\frac{{{\text{A}}_{\text{eff}} }}{{{\text{d}}_{\text{eff}} }}} \right)_{\text{Top}} }}$$
(8)
where, \(\upvarepsilon_{{{\text{r}}_{ \, } }}\) (as per Eq. (3)) is the relative permittivity of the material between the electrodes, \(\upvarepsilon o\) is the vacuum permittivity, Aeff is the effective overall surface area of top and side, and deff is the effective overall distance between electrodes as shown in Fig. 5 as per Eq. (8).
Surface characterization of different layers of the biosensor
In this study, the purpose of the SAM layer is to insulate the electrodes and prevent them from short circuiting [33]. The functionality and the presence of the SAM layer are confirmed by AFM image of the Thiourea coated gold electrodes. Figure 6 shows the AFM image of the electrodes having Thiourea layer deposited on top of it. The increment in the net vertical height (~ 20 nm) of the electrodes along with the surface roughness confirms the formation of the SAM layer. The SAM layer insulation was also confirmed using electrical measurements. The carboxylic functionalized gold nanoparticles were incubated, and surface activated using EDC/NHS coupling. The CA-125 antibodies are then added and incubated on top of the gold nanoparticles. Figure 7 shows the AFM images of the gold nanoparticles and the antibodies present on top of the gold nanoparticles.
CA-125 antigen solution flow in microchannel
In this experiment, a microchannel with the width of ‘W’ (300 μm) and depth of ‘h’ (107 μm) is used to generate the microfluidic flow on the sensing platform as shown in Fig. 8a. The microchannel is fabricated using PDMS, which is hydrophobic in nature. The hydrophobic nature of PDMS is converted to hydrophilic using the plasma treatment. The flow of the antigen solution in the microchannel due to the capillary effect generates a shear on the sensing surface. The shear stress at the surface of sensing is defined by the change in the antigen solution flow velocity (Ux) with respect to the channel height at the channel surface (y = 0), by assuming that the flow of the antigen solution as the poiseuille flow in the infinite parallel plates due to the high aspect ratio and the insignificant side wall effect.
$$\tau = \mu \left. {\frac{{\partial {\text{Ux}}}}{{\partial {\text{y}}}}} \right|_{\text{y = 0}} \approx \mu \frac{{ 6 {\text{Q}}}}{{wh^{2} }}$$
(9)
where the flow rate of the antigen solution is measured as Q (0.2 μl/s) using a high-speed camera (Phantom V-7.3), with the dynamic viscosity (μ) of the antigen solution (8.8 × 10−4 pa s) the width of the microchannel is W (300 μm), the depth of the microchannel is h (107 um) as shown in Fig. 8b. Thus, the shear stress (τ) is calculated as 0.307 pa as per Eq. (9). The shear stress has influences on the stability of the immobilized CA-125 antibodies on top of the sensing surface with gold nano particles and the corresponding effect on sensitivity are explained in detail in Sect. 3.4.5 of the paper.
Electrical characterization
Capacitance measurement of different layers of biosensor
The capacitance is measured at various stages consisting of different sub-layers. All the measurements were taken using a two-point probe station and the dielectric parameters were calculated using Agilent 4284A Precision LCR meter. The frequency range was taken from 10 to 100 kHz for all the sub-layers using 10 kHz steps.
Figure 9 shows the plot of capacitance variation over frequency for different layers of the sensor. The highest capacitance of the bare interdigitated electrodes was 9.38 pF at 10 kHz and the lowest was 8.70 pF at 100 kHz. The capacitance values of the SAM layer (Thiourea) was observed to be lower than the bare electrodes. The highest value recorded was 9.06 pF at 10 kHz and the lowest was 8.47 pF at 100 kHz. The potential reason is the higher charge transfer resistance of the SAM layer which directly affects the real part of the impedance. This increase in the resistance directly influences and increases the net impedance. Because of this phenomenon, the net capacitance of the circuit decreases over frequency [35, 36]. The higher permittivity of the gold nanoparticles resulted in higher capacitance than that of both bare electrodes and the SAM layer, giving values of 9.62 pF at 10 kHz and 8.76 pF at 100 kHz. The capacitance measurement at the immobilized CA-125 antibody layer was 11.94 pF at 10 kHz frequency and then reduced by increasing frequency, down to 9.36 pF at 100 kHz frequency as shown in Fig. 9.
Capacitance measurement of a CA-125 antigen conjugation with CA-125 antibodies immobilized on biosensor
The study used a solution of PBS solvent with and without CA-125 antigens respectively. First for the baseline study, plain PBS solution without CA-125 antigens was measured with CA-125 antibodies coated on the nano electrodes. A drop of PBS solution (approximately 1 µl) was placed on the biosensor. The PBS solution capacitance measurements were taken in the frequency range from 10 to 100 kHz. The capacitance values almost remained unchanged over the entire frequency range. The capacitance curve of the plain PBS solution was regarded as the ‘Baseline’. The highest and lowest capacitive values of the ‘Baseline’ curve were measured to be 96.90 pF and 69.19 pF respectively.
The next for CA-125 antigens case, a 1 μl droplet of CA-125 antigen solution is placed on the biosensor. The capacitance measurements of the antigen and antibody conjugation are taken from the same range of frequency. The capacitive values of the CA-125 antigen solution case with CA-125 antigen–antibody conjugation, ‘after Ag–Ab conjugation’ curve was measured to be 822.93 pF at 10 kHz and changed to 342.18 pF at 100 kHz. The antigens and the antibodies interaction are very selective and specific. The specific antigen and antibody interactions form a complex which increases the net molecular size. The change in the size of the complex which has a unique property of electrical charge, disturb or interfere the distribution of the charges present in the dielectric medium. The antigen–antibody complex which has unique property of electrical charge creates a change in the distribution of charges within the dielectric region and forms a dipole moment. Because of this phenomenon, the polarization is created due to the dipole–dipole interaction within the dielectric interface [33, 34] substantially leads to a high increase in capacitance. Also, the dielectric values of each antigen–antibody complex over the range of frequencies have its unique variation. The measured impedance or capacitance of the biosensor varies with the change in dielectric properties on sensor surface. The change in the dielectric properties directly influences the change in the capacitance over a range of frequencies. The highest capacitance values were observed at 10 kHz for both ‘Baseline’ and after the Ag–Ab conjugation in the selected frequency range. The capacitance of the ‘Baseline’ is around 96.90 pF and is increased to a value around 822.93 pF after the antigens conjugation at 10 kHz as shown in plot of Fig. 10. The significant change in the capacitance values represents the conjugation of the CA-125 antigens and antibodies.
Capacitance measurement comparison of antigen–antibody interactions on plain interdigitated electrodes and gold nanoparticle layered interdigitated electrodes, respectively
The gold nanoparticles-based sensing platform which was coated with gold nanoparticles on the interdigitated electrodes showed the enhanced capacitance during antigen–antibody interaction, compared to plain interdigitated electrodes, as seen in Fig. 11. Although there are various noble metals which can serve the purpose for biosensing, the gold nanoparticles are found to be promising and better for biosensing due to its unique surface chemistry, high electron densities, chemical inertness and it possesses both good electrical and optical properties [20]. The carboxylic coated gold nanoparticles provide higher surface to volume ratio for the immobilization of the antibodies. The gold nanoparticles provide enhanced stability due to better orientational freedom for the antibodies attachment. This phenomenon not only provides better stability but also results in accumulating more antibodies for the antigen–antibody conjugation. The highest capacitance of both sensing platforms is measured at 10 kHz and are found to be 822.93 pF for gold nanoparticles coated interdigitated electrodes and 296.09 pF for plain interdigitated electrodes. The capacitance of the carboxylic gold nanoparticles is found to be almost three times the capacitance of the plain interdigitated electrodes. Two factors may be contributing to this phenomenon. The first explanation is due to the enhanced orientation freedom and higher surface to volume ratio of the gold nanoparticles as compared to the plain interdigitated electrodes. This characteristic results in increasing the net amount of the antibodies. As a result, the capacitance signal response is higher for gold nanoparticle coated interdigitated electrodes when compared to plain interdigitated electrodes [42,43,44]. Another explanation is the surface coverage of the carboxylic functionalized group on top of the nanostructure or nano-elements for covalent conjugation. Although the plain interdigitated electrode sensing mechanism also used covalent bonding for antibody binding, the gold nanoparticles provide much more surface area of the electrodes. This resulted in capturing a significantly greater number of antibodies using covalent bonding for the gold nanoparticles-based interdigitated electrodes.
Capacitance measurement comparison of antigen–antibody interaction with multiple concentrations of antigens
The capacitance signal response was captured during CA-125 antigen–antibody conjugation with different concentrations of CA-125 antigens, as shown in Fig. 12. The CA-125 antigens are aliquotted into different concentrations: 84,000 U/ml, 35,000 U/ml, 3500 U/ml, and plain PBS (without CA-125 antigens). The CA-125 antigens of different concentrations were measured using the static drop condition on the gold nanoparticle coated interdigitated electrodes. The antibodies immobilized on the gold nanoparticles interact with the CA-125 antigens and generate the corresponding capacitance signal response. The capacitance signal response during the antigen–antibody interaction is as high as 822.93 pF with an antigen solution of 84,000 U/ml and the signal response drops to 706.91 pF, 640.5 pF and 96.90 pF for the concentrations of 35,000 U/ml, 3500 U/ml and PBS (without antigens) respectively at 10 kHz frequency. The capacitance signal response of the PBS solution without any antigens was captured to confirm that the change in signal difference is caused only due to the antigen–antibody interaction. The change in the capacitance signal is directly proportional to the concentration of the antigens in the sample. The signal response of antigen–antibody interaction for lower concentrations of antigens was observed due to the low number of antigens interacting with the antibodies that were immobilized on the gold nanoparticle based interdigitated electrodes. The capacitance signal for all the concentrations decreased as the frequency increased. As predicted by electrochemical theory, the change in the capacitance signal between two different concentrations of antigens at a frequency was almost same (over the frequency range of 10 kHz to 100 kHz).
Capacitance measurement comparison of CA-125 antigen–antibody conjugation at static and microfluidic flow condition
The plot in Fig. 12 shows the variation in the signal response between the static condition and the microfluidic flow condition during the CA-125 Ab–Ag conjugation. The carboxylic gold nanoparticles sensing platform without the microchannel (static drop condition) resulted in consistently higher capacitance values because there is no external disturbance on antigen and antibody interaction whereas the microchannel flow has the external effect by the shear of the flow. The highest capacitance is recorded to be 822.93 pF at 10 kHz and the lowest is 342.18 pF at 100 kHz.
Microfluidic flow condition of the biofluid sample with CA-125 antigens
To understand the sensitivity variation due to the microfluidic flow, a biofluid sample with the exact same composition to the static drop condition was passed through the microchannel at a constant flow rate (0.2 μl/s) over the sensing platform. The capacitance values were measured during the antigen–antibody interaction when the biofluid was flowing in the microchannel. The capacitance measurement in the microfluidic flow condition during CA-125 antigen–antibody interaction was measured as 807.30 pF at 10 kHz frequency and gradually decreased to 234.51 pF at 100 kHz frequency as shown in Fig. 13. The capacitance measurement during the CA-125 antigen–antibody interaction has decreased from 822.93 pF for the static drop condition to 342.18 pF at 10 kHz for the microfluidic flow condition as shown in Fig. 13.
The capacitance was recorded from the highest value of 807.30 pF to the lowest value of 234.51 pF within the frequency range from 10 to 100 kHz during the flow of the antigen solution in the microchannel. The tight confinement of the microfluidic flow exerts high surface shear stress which impact the stabilization of the antibodies that are bonded to the sensing platform [37, 38]. The shear forces applied by the fluid on the antibodies that are bonded to the electrode sensing platform in the microchannel induce mechanical breakage of the weak bonds of the antibodies with the electrode [39,40,41]. The breakage of bonds of the antibodies with the sensing surface could influence the stability of the immobilization of antibodies. So due to the existence of shear in the microfluidic flow condition, the stability of the CA-125 antibody would be significantly lower, which could directly influence the sensitivity. So due to lack of any shear in ‘static’ condition, the stability of the CA-125 antibody was significantly higher and directly enhanced the sensitivity.
Capacitance variation during CA-125 antigen antibody interaction at different conditions (at 20 kHz frequency)
Figure 14 shows the change in the capacitance of antigen–antibody interaction at different conditions of the sensing platform (plain interdigitated electrodes and gold layered interdigitated electrodes) and different flow conditions (static drop condition and microfluidic flow condition) at 20 kHz frequency.
As shown in Fig. 14, the change in the capacitance from the static drop condition to microfluidic condition for plain electrode is 54.95 pF and for gold nanoparticle coated electrodes is 217.85 pF. As explained in the earlier sections, the gold nano particles (GNPs) coated electrodes has the higher sensing signal than the plain electrodes due to the enhanced antibodies immobilization on the gold nano particles with the high surface to volume ratio and orientation freedom. Also, GNPs has the higher resistance to shear flow than plain interdigitated electrodes for microchannel flow.