Precise evaluation of liquid conductivity using a multi-channel microfluidic chip and direct-current resistance measurements

Sensors & Actuators: B. Chemical 297 (2019) 126810

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Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb

Precise evaluation of liquid conductivity using a multi-channel microfluidic chip and direct-current resistance measurements

T

Hyowoong Noha,1, Junyeong Leea,1, Chang-Ju Leea, Jaedong Junga, Jaewoon Kanga, ⁎ Muhan Choia, Moon-Chang Baekb, Jae Hoon Shima, Hongsik Parka, a b

School of Electronics Engineering, Kyungpook National University, Daegu 41566, Republic of Korea School of Medicine, Kyungpook National University, Daegu 41944, Republic of Korea

ARTICLE INFO

ABSTRACT

Keywords: Liquid conductivity Interface resistance Transmission line method Direct-current resistance Multi-channel microfluidic chip Effective channel region

In various research fields related to electrochemistry, such as biosensors and energy storage engineering, the conductivity of an electrolyte solution is one of the most fundamental parameters that determines device design and performance. The simplest procedure for obtaining the conductivity of a liquid is to (i) measure the directcurrent resistance of liquid whose volume and dimensions is well-defined and (ii) calculate the conductivity from the measured resistance. However, this method has not been widely used because the measured resistance always includes electrode-electrolyte interface resistance and the extraction of a correct conductivity is difficult. In this study, we designed a multi-channel microfluidic chip that can remove the effects of interface resistance in determining the intrinsic resistance of a liquid and developed a method for the precise evaluation of liquid conductivity. We observed that the interface resistance was significantly affected by the channel length and applied voltage. We measured the intrinsic resistance of phosphate-buffered saline (PBS), conductivity standard solutions, and cell culture media using the proposed multi-channel chip including different-length channels, and we removed the effect of voltage-dependent interface resistance by applying a constant current source for the measurement and determined the precise conductivities of these solutions. We verified the accuracy of the proposed method by comparing the results with the conductivity measured using electrochemical impedance spectroscopy. The proposed method was also applied to determine the zeta-potential of charged nanoparticles with an average diameter of 110 nm. This simple method for determining liquid conductivity could be widely employed in various electrochemical applications.

1. Introduction Electrical conductivity is one of the fundamental parameters of an electrolyte solution, thus the accurate measurement of liquid conductivity is important in electrochemical research and applications. For examples, the conductivity of electrolyte solution determines various measures of battery performance, such as lifetime, charging/discharging speed, and power capability [1–3]. Conductivity can also be used to determine the ion concentration or ion mobility of an electrolyte solution [4–6]. The liquid conductivity is an important parameter in the design of electrophoresis-based microfluidic chips [7,8] and in research on the compositional changes of biological fluids [9,10]. The conductivity of a liquid is typically extracted from the frequency-dependence of liquid impedance measured by electrochemical impedance spectroscopy (EIS) [11–14]. In this measurement approach,

the impedance of an electrode-liquid-electrode system is measured by applying an alternating-current (AC) signal with varying frequency. This technique has significant advantages in that the effect of the interface resistance between the electrode and liquid can be removed and that the effect of electrolysis is negligible during the measurement process because of the use of AC [15–17]. However, it has been reported that the ideal equivalent circuit model (i.e. Randles equivalent circuit) used for the analysis of frequency-dependent impedance may produce results that are not always accurate for all types of liquid in an electrode-liquid system [18]. Thus, the complication with this approach is that an appropriate circuit model needs to be selected to ensure precise measurement. In addition to this, EIS requires a relatively long measurement time [19–21] and typically requires a relatively large solution volume (> 5 ml) for reliable measurement [22–24]. To improve the performance and effectiveness of the measurement and

Corresponding author. E-mail address: [email protected] (H. Park). 1 These authors contributed equally to this work. ⁎

https://doi.org/10.1016/j.snb.2019.126810 Received 28 February 2019; Received in revised form 8 July 2019; Accepted 10 July 2019 Available online 14 July 2019 0925-4005/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. (a) The schematic and image of a multi-channel microfluidic chip. This chip includes five types of liquid channels with different channel lengths. The electrodes and liquid channels are models as a series connect of channel resistance (Rch) and two interface channel (Rint). (b) Simulation results of electric field distributions in 20-mm-length channel (left) and 60-mm-length channel (right) of the multi-channel microfluidic chip. The effective channel length (Lch) is defined as the length of channel regions where the electric field is uniform. Lch is shorter than the physical channel length (L). (c) The normalized electric field [Ex(x)/Ex(x = L/ 2)] in the 20-mm-length channel along the length direction (x-direction) and (d) the normalized electric field [Ex(y)/Ex(y = W/2)] in the channel along the width (W) direction (y-direction). The electric field is uniform in the liquid regions from the points 4 mm away from the electrode edges. The length of this nonuniform-field regions near electrode is not dependent on the physical channel length if the channel width is constant.

analysis of conductivity, various EIS approaches have been proposed, such as Fourier transform electrochemical impedance spectroscopy (FTEIS) [19]. Small-volume conductivity cells (˜10 μl) for EIS have also been developed and commercialized, even though there are some issues with measurement accuracy. Another method for evaluation of liquid conductivity is the direct measurement of liquid resistance using a direct-current (DC) signal [25,26]. The resistance of the liquid is the ratio of applied (or measured) voltage to measured (or applied) current (i.e. Ohm’s law), and the conductivity of the liquid can be simply calculated from the resistance and the dimensions (length and cross-sectional area) of the

liquid volume. However, this method is not widely used because of two critical issues. In most cases, the intrinsic liquid resistance differs from the measured resistance because the measured resistance always includes electrode-liquid interface resistance. Thus, using a simple twoterminal DC measurement system, it is difficult to separate the liquid resistance and interface resistance from the total measured resistance. Another complication with this approach is that electrolysis occurs in the liquid when subject to applied DC voltage. Electrolysis may affect the measurement of resistance if it significantly changes the ion concentration in the liquid or generates bubbles on the electrodes [27]. Therefore, the use of conductivity measurement approaches based on 2

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DC voltage/current has been typically limited to the measurement of the conductivity of dielectric (i.e. low-conductivity) liquids because the effects of interface resistance and electrolysis are minimized due to the large resistivity and low ion concentration of these liquids [25,26]. Unlike liquids, however, the conductivity of solid-state materials is typically determined using DC measurement approaches. The resistance of a solid-state material is measured using a DC signal, and the conductivity is simply calculated from the measured resistance and the sample dimensions. However, the DC-based measurement of solid-state materials has a similar problem as that seen for liquids when the electrode-material interface resistance, known as contact resistance, cannot be neglected. In particular, for most semiconductor resistors, the metal-semiconductor contact resistance is considerable, so the conductivity of the semiconductor cannot be precisely evaluated using a simple DC-based approach. Because of this, evaluation of conductivity (or resistivity) of a semiconductor, the transmission line method (TLM) is widely used [28–31]. In this method, the resistances of multiple metal-semiconductor-metal devices that have identical metal-semiconductor contacts and different semiconductor lengths are measured. The differences in the measured resistances of these multiple devices are only dependent on the difference in length of the semiconductors because the contact resistance is the same for all devices. Therefore, intrinsic semiconductor conductivity can be determined from the slope of the plot of the measured resistance versus the semiconductor length. Contact resistance is also determined from the y-intercept of this plot. In this study, we applied the concept of TLM for the evaluation of liquid conductivity. We designed and fabricated a multi-channel microfluidic chip that had multiple liquid channels with varying channel lengths and an identical electrode structure. We also developed a measurement and analysis method for the evaluation of liquid conductivity. Using this method, we measured the electrical properties of various electrolyte solutions (phosphate-buffered saline (PBS), conductivity standard solutions (0.01 M, 0.1 M, and 1 M KCl), and cell culture media). We were able to determine liquid resistance and electrode-liquid interface resistance separately by measuring the total resistance of the channels of varying length. Based on the intrinsic liquid resistance and dimensions of the liquid channels, we were able to calculate the conductivity of the solutions. During this experiment, we observed that the interface resistance was dependent on the liquidchannel length and applied voltage. To remove the effect of the electricfield dependence of interface resistance, we used a constant current source for our measurements, which guaranteed identical electrode-liquid interface conditions for each of the channels. The results of the analysis of the conductivity of the target solutions supported the accuracy of our proposed approach. In addition, we also measured the conductivity of the same solutions using commercial EIS equipment and compared the EIS results with those obtained from the proposed method. Finally, we applied our method to the zeta-potential analysis of charged nanoparticles.

(PDMS) channels to a glass substrate. First, we fabricated a silicon mold for the fabrication of the PDMS (Dow Corning Corp.) channels. A 6-inch silicon wafer with a thickness of 675 μm was cut into pieces that met the required dimensions for the five channel lengths using a dicing machine, and these pieces were assembled on a 4-inch silicon wafer with 5-μm-thick polyimide tape as an adhesion layer. Trimethylchlorosilane (TMCS, Daejung Chemicals & Metals) was coated on the fabricated mold as a release agent for 30 min [32–35]. PDMS mixed with a curing agent at a 10:1 wt ratio was poured onto the mold and cured for 4 h at 80 ℃, and two inlet/outlet holes with a diameter of 2 mm were made in the cured PDMS. The center of the inlet/outlet holes was located 1.5 mm from the end of channels. A glass plate (100 mm × 100 mm) and the cured PDMS were activated with oxygen plasma (30 W power for 20 s) and bonded to each other [36,37]. An image of a fabricated multi-channel microfluidic chip is shown in Fig. 1(a), in addition to a schematic diagram of two electrodes and the target liquid in a single channel and the resultant simple equivalent circuit. The electrodes and liquid channels were modeled by a channel resistance and two interface resistances connected in series. The channel resistance (Rch) was defined as the liquid resistance in the ‘effective’ channel region, and the interface resistance (Rint) was defined as the resistance corresponding to the electrode-liquid interface region. The total resistance measured by a DC signal was thus the sum of the channel resistance and the two interface resistances:

Rmeas = R ch + 2Rint =

Lch 1 Lch + 2Rint = + 2Rint A A

(1)

2. Experiments

where ρ is the liquid resistivity, σ is the liquid conductivity, and A is the cross-sectional area of the channel. Liquid conductivity can be calculated from the liquid channel resistance and the channel dimensions (length and cross-sectional area). The relation between the channel resistance and conductivity given in Eq. (1) is valid only if the electric field is uniform in the effective channel region. Therefore, it is important to appropriately define the effective channel region. As shown in Fig. (1), for DC measurements, two platinum (Pt) tips with a diameter of 1 mm were used as electrodes. These electrodes were probed into the solution through the circular inlet and outlet. The contact in the liquid is cylindrical in shape with a diameter smaller than the channel width. This means that there are liquid regions in which the electric field is not uniform near the electrodes. We defined this region as a ‘nonuniform-field region’ in this study. The basic concept of the evaluation method proposed in this study is to (i) measure the resistance of multiple channels with various channel lengths, (ii) compare the difference in the measured resistances that arises only due to differences in the length of the liquid channels, and (iii) calculate the conductivity from this change in length-dependent resistance. Consequently, the results of this evaluation approach are not affected by the definition of the effective channel length as long as the electric field is uniform in the effective channel. Conductivity is calculated from ΔRch/ΔLch, which is the same as ΔRmeas/ΔLch because it is assumed that the Rint of all channels is the same in this evaluation.

2.1. Fabrication of the multi-channel microfluidic chip

2.2. Simulation of the electric field distribution in the channels

To determine the conductivity of a liquid, it is important to measure the intrinsic resistance of the liquid channel (Rch) without the effect of electrode-liquid interface resistance (Rint). Our idea for extracting the liquid channel resistance from the measured resistance (Rmeas = Rch + 2Rint) was to measure multiple liquid channels that have identical electrode structures but different channel lengths. To achieve this, we fabricated a multi-channel microfluidic chip that contained liquid channels of five different lengths on a single chip. A schematic diagram of the proposed multi-channel microfluidic chip is shown in Fig. 1(a). The length (L) of the five channels were 20, 30, 40, 50, and 60 mm and the width (5 mm) and depth (680 μm) of all channel was the same. We fabricated the multi-channel chip by bonding polydimethylsiloxane

To extract the liquid conductivity based on Eq. (1), we should define the effective liquid channel length excluding the nonuniform electricfield regions near the electrodes. We simulated the electric field distribution in each channel of the multi-channel chip under a constant voltage. We used the multi-physics software (COMSOL) to investigate the field distributions in all channels with different lengths (L = 20, 30, 40, 50, and 60 mm). Here, L is the physical length of the channels including the inlet/outlet regions. Fig. 1(b) shows the simulation results for the 20-mm and 60-mm channels. In this simulation, it was assumed that the channels were filled with a liquid whose conductivity and dielectric constant was 15 mS/cm and 80.4, respectively. This conductivity and dielectric constant values correspond to the 3

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1 ± 0.05 cm−1 [38].

characteristics of PBS, which was used in this study. Fig. 1(b) shows the electric field distributions in the liquid channels under an applied voltage of 5 V. In this electrode-channel-electrode structure, the electrodes (diameter = 1 mm) were positioned at the center of inlet/outlet holes, which were located 1.5 mm from the edges (i.e. the endpoints of the physical channel length) of the channels. The direction of the red arrows in the channel indicates the direction of the electric field and the color in the liquid channel represents the electric field strength (Fig. 1(b)). These simulation results show that the direction and strength of the electric field near the electrodes were nonuniform.

2.5. Zeta-potential analysis of charged nanoparticles We applied the method proposed in this study to the zeta-potential analysis of charged nanoparticles in a liquid channel. It is known that the zeta potential of charged nanoparticles (ζp) is determined by the drift velocity (electrophoretic velocity, Uep) of the nanoparticles and the electric field (E) applied to the nanoparticles in the liquid channel [42]. In most cases, the electric field cannot be simply calculated from an applied voltage because there is voltage drop at the electrode-liquid interface. However, if we know the conductivity of the nanoparticle liquid, the electric field can be simply calculated from the conductivity and current density. For this reason, in the zeta-potential analysis of nanoparticles, it is vital to accurately measure the conductivity of the liquid. In this study, we evaluated the zeta potential of polystyrene nanoparticles (FCDG002, Bangs Laboratories Inc.) suspended in PBS. The polystyrene nanoparticle was labelled with fluorescent dyes and the average diameter of the nanoparticles was 110 nm. First, we evaluated the conductivity (σ = 15.2 mS/cm) of the nanoparticle liquid using the multi-channel chip. We applied a constant current source to the 60-mm-length channel of the multi-channel chip. We applied a constant current source to the channel, and the movement of the fluorescent nanoparticles was observed using a confocal microscope (LSM 800, Carl Zeiss). Based on this movement, the electrophoretic velocity of the nanoparticles (Uep) was measured and electrophoretic mobility of the nanoparticles (μep) could be calculated by the following relation:

2.3. Measurement procedure for liquid resistance using the multi-channel microfluidic chip In this study, we determined the conductivity of PBS, KCl (0.01 M, 0.1 M, and 1 M) in H2O, and cell culture media (MEM, DMEM, and RPMI-1640). PBS is a buffer solution that is commonly used in biological research. The composition and concentration of the PBS solution used in this study were NaCl of 137 mM, KCl of 2.7 mM, Na2HPO4 of 10 mM, and KH2PO4 of 1.8 mM. The KCl aqueous solutions are conductivity standard solutions for which the conductivity values at specific temperatures are well known. The reference conductivity of the KCl solutions (0.01, 0.1, and 1 M) were 1.41, 12.88, and 111.8 mS/cm, respectively. MEM, DMEM, and RPMI-1640 are cell-culture media commonly used in biological research. To evaluate the conductivity of these solutions, we measured the resistances of the multi-channels filled up with the target solutions. Two electrodes (i.e. the Pt tips) were inserted in the liquid through the inlet/outlet holes of the channels, and a constant voltage (or constant current) was applied to the channel through the electrodes and the current (or voltage) measured. A source measurement unit (B2901A, Keysight) was used simultaneously as the power supply and for measurement. To ensure stable measurements, the current (or voltage) was measured 10 s after the constant voltage (or constant current) had been applied.

µep =

Uep E

=

0 r p

(2)

where η is the viscosity of the liquid, ε0 is the vacuum permittivity, and εr is the dielectric constant of the liquid. The zeta potential of the nanoparticles was then calculated using Eq. (2).

2.4. Electrochemical impedance spectroscopy for the measurement of liquid conductivity

3. Results and discussion

As mentioned in the previous section, we evaluated the conductivity of a standard solution (KCl) to verify the accuracy of the method proposed in this study. In addition, we also compared the results from the proposed method with the conductivity of the solutions evaluated by EIS which is the most widely used method for liquid conductivity measurement. We measured the frequency-dependent impedance and extracted the conductivity of the target solutions using a commercial conductivity cell (HTCC, Bio-Logic Science Instruments) and EIS instrument (VMP-300, Bio-Logic Science Instruments) [38]. The same solutions as those measured using the multi-channel chip (PBS, KCl, and cell culture media) were filled in the conductivity cell (volume = 2 ml), which contained Pt plate electrodes (electrode gap = 3 mm). Sinusoidal AC voltage with varying frequency was applied to the cell and the resistance of the liquid was determined from the impedance plot (known as a Nyquist plot) in a complex plane. For the analysis of the impedance data collected using EIS, a Randles equivalent circuit was used as the model for the electrode-liquid interface [39–41]. The amplitude of the AC signal applied to the liquid was 14 mV and the frequency range was swept from 1 MHz to 1 Hz [4,11–14]. The conductivity was calculated from the measured resistance (R) and the cell constant (K) for the conductivity cell used in this measurement (σ = K/R). In EIS, the cell constant (K) is used for the calculation of liquid conductivity from the measured resistance. This constant is typically determined by the area of electrode and the distance between the electrodes when the volume of liquid is well confined between two electrodes. In case a conductivity cell is larger than the electrode dimensions, the cell constant would include a term for calibration of the conductivity calculation. The cell constant of the conductivity cell used in this measurement was

3.1. Definition of interface resistance and the effective channel region As explained in Section 2.1, liquid conductivity can be calculated from the difference in channel resistance between channels of different length without including the effect of interface resistance [ΔRmeas/ΔLch = ΔRch/ΔLch = 1/(σ∙A)]. This is valid only if the electric field (and thus current density) is uniform in the ‘effective’ liquid channel; therefore, the length of the effective channel needs to be correctly defined. The DC resistance of each liquid channel can be modeled as a series connection of two interface resistance and channel resistance (Fig. 1(a)). Here, we defined channel resistance as the resistance of the uniform-field channel region where the electric field is uniform. The interface resistance included (i) the interface resistance caused by the electrical double layer at the electrode-liquid interface and (ii) the resistance of the nonuniform-field channel regions near the electrodes. These definitions are similar to those used for metal-semiconductor-metal resistance. The resistance of most semiconductor resistors is modeled as a series connection of two contact resistances (corresponding to the interface resistance in this work) and the semiconductor channel resistance [31]. Contact resistance includes metal-semiconductor junction resistance and the resistance of the semiconductor region in which current density (i.e. the electric field) is nonuniform. The simulation results in Fig. 1(b) show that the electric field was not uniform in the liquid regions near the electrodes for either the 20mm channel (left) or the 60-mm channel (right) in the multi-channel microfluidic chip. Because the effective channel length (Lch) is defined as the length of the channel region where the electric field is uniform, Lch is shorter than the physical channel length (L). Fig. 1(c) shows the 4

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normalized electric field [Ex(x)/Ex(x = L/2)] in the 60-mm-length channel along the length direction (i.e. the x-direction). The electric field strength at all positions in the channel was normalized by the electric field strength at the middle of the channel in order to compare the electric field distributions in the different-length channels. For example, the actual electric field in the 20-mm-length channel (distance between electrodes = 16 mm) was more than three times larger than that of 60-mm-length channel (distance between electrodes = 56 mm). In this field analysis, the x-component of the electric field is of interest because we calculated conductivity from the resistance and liquid dimensions (length and cross-sectional area) assuming that the current flows only in the length direction. As shown in the plot, the electric field was uniform along the length direction in the middle of the channel region, but the strength of the electric field sharply increased near the electrodes because the diameter of the electrodes was smaller than the channel width. These results indicate that the electric field is uniform in the channel regions from points 4 mm away from the electrode edges [Ex(x = 4)/Ex(x = L/2) < 1%]. To calculate conductivity, the electric field should also be uniform along the width direction. Fig. 1(d) shows the normalized electric field [Ex(y)/Ex(x = L/2, y = W/2)] in the channel along the width (W) direction (i.e. the y-direction). This plot shows that the electric field along the width direction is also uniform in the uniform-field region. However, the electric field is not uniform along the width direction near the electrodes. For example, at the edge of the electrodes (x = 2 mm and x = 58 mm), the normalized electric field at the center of the channel width [Ex(x = 2 mm, y = W/2)/Ex(x = L/2, y = W/2)] is about five times larger than that at the edges of the channel width [Ex(x = 2 mm, y = 0)/ Ex(x = L/2, y = W/2)]. Because the changes in the electric field direction and strength are dependent on the difference in size between the electrode diameter and channel width, the length of the nonuniform-field regions near the electrodes is not dependent of the physical channel length (see Supplementary materials, Fig. S1). Based on these results, we defined the effective channel length as the length of the liquid channel region 4 mm away from the two electrode edges. The effective channel length is thus 12 mm smaller than the physical channel length [Lch = L – 2×(LE + D/2 + Lint) = L – 12 mm], where LE is the distance from the center of the electrode to the end of the physical channel (1.5 mm), D is the diameter of the electrode (1 mm), and Lint is the length of the nonuniform-field region (4 mm).

conductivity of the measured PBS solution, with the conductivity values increasing as the DC voltage increased. There are three points we need to consider with respect to these results. First, the relation between Rmeas and Lch was clearly linear. Second, given that conductivity is a material parameter, the calculated conductivity should not have a dependence on voltage as long as the applied voltage does not change the intrinsic electrical properties of the PBS solution. Third, the evaluated conductivity for PBS was considerably smaller than the conductivity of PBS reported by previous studies (15–17 mS/cm) [43–46]. These results imply that measurements based on a constant voltage source may cause errors in determining the conductivity of a liquid. In our approach, conductivity is calculated based on the assumption that Rint is constant for all five channels with different channel lengths. However, if Rint is dependent on Lch, this method cannot correctly evaluate the conductivity. In this case, Rmeas vs. Lch is not linear, as shown in Fig. 2(a), and the conductivity extracted from the linear fit is not correct. A more complicated situation would be if this Lch-dependence is dependent on the applied voltage. In this case, the conductivity calculated using a linear fit has a voltage dependence as shown in Fig. 2(b). To verify these effects, we estimated the interface resistance of the five PBS channels and investigated the dependence of interface resistance on channel length and applied voltage. For this estimation, we calculated Rch by using the effective channel length and the known conductivity value (15 mS/cm) of PBS. Fig. 2(c) presents a plot of the interface resistance as a function of the effective channel length for different voltages. The results show that, in general, the interface resistance increased as the channel length increased. We attribute this Lch-dependence of Rint to the difference in the interface voltage (Vint) for the channels with different lengths. Under the same constant voltage (V), the interface resistance decreases as the channel length increases because the voltage drops across the channel (Vch) increases (V = Vch + 2Vint). Here, the interface voltage (Vint) means the voltage drop across the interface region, including the interface electrical double layer and the nonuniform-field region. It is known that the DC interface resistance at an electrode-liquid interface is related to the potential gradient at the electrical double layer and charge transport (i.e. ions and electrons) via the charge-transfer reaction (i.e. the transfer of electrons via a redox reaction at the interface), charge adsorption, and charge mass transport (i.e. ion diffusion due to the concentration gradient and ion drift due to the electric field) [27,47]. Because these charge transfer mechanisms are associated with the potential gradient and electric field, the interface resistance can be changed by the interface voltage induced at the interface region [47]. The plot in Fig. 2(c) also indicates that the degree of Lch-dependence of Rint is affected by the applied voltage. When the applied voltage is larger, the rate of change for Rint is smaller. This result can explain the voltage-dependence of the calculated conductivity in Fig. 2(b). Fig. 2(d) presents a plot of interface resistance as a function of the applied voltage. It clearly shows that the interface resistance significantly decreased with increased voltage due to an increased interface voltage.

3.2. Measurement of liquid conductivity using a constant voltage source Using the proposed multi-channel chip and evaluation method, we determined the conductivity of the PBS solution. First, we measured the resistance of the five channels with different lengths containing the PBS solution. The most commonly used method for DC resistance measurement is applying a constant voltage source to a resistor and measuring the current flowing through the resistor. This simple DC measurement approach is predominantly used for the measurement of solidstate resistors. We applied various DC constant voltages (2.5, 3.0, 3.5, and 4.0 V) to the channels and measured the current. The plot of the measured resistance of the channels versus the effective channel length is shown in Fig. 2(a). As the effective channel length (Lch = L – 12 mm) increased, the measured resistance increased linearly, although this linearity was not perfect. Because the increase in the resistance was due only to the increase in the PBS channel length, we could calculate the conductivity of PBS using the slope of the plot:

=

1 A

Lch 1 = Rch A

Lch 1 1 = Rmeas A slope

3.3. Measurement of liquid conductivity using a constant current source As shown in Fig. 2, the conductivity measurement using a constant voltage source may produce incorrect results because the assumption that the Rint is the same for all channels is not valid. To overcome this problem, we measured the channel resistance by applying a constant current source. In a series circuit, the current flowing through the circuit is always constant when a constant current is applied. This means that the current through the liquid channel (Ich) and the current (Iint) through the interface region is not dependent on the channel length if a constant current (I) is applied to channels with different channel lengths (Iint = Ich = I). Therefore, we can expect interface resistance to be the same for channels of different lengths under the same constantcurrent condition because (i) the current through the interface is the

(3)

The slope of the plot of the measured resistance versus the effective channel length was obtained from the slope of linear fitted curves for the data. It is notable that the slope of the fitted lines decreased as the applied voltage increased. This means that the calculated conductivity was dependent on the DC voltage. Fig. 2(b) shows the calculated 5

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Fig. 2. (a) The measured resistance of the channels versus the effective channel length. We applied various DC constant voltages (2.5, 3.0, 3.5, and 4.0 V) to the channels. The slope of the fitted lines decreased as the applied voltage increased. (b) The calculated conductivity of the measured PBS solution. The conductivity values increased as the DC voltages increases. (c) The interface resistance as a function of the effective channel length under different voltages. The degree of Lch-dependence of Rint is affected by the applied voltage. (d) The interface resistance as a function of the applied voltages. The interface resistance significantly decreased by the increased voltage.

same, and (ii) the current through the interface is a function of the interface voltage drop (Vint). Here, (i) and (ii) means that Vint is the same for all five different-length channels if the same constant current is applied. To measure the resistance of the channels, we applied various DC constant currents (200, 240, 280, 320, and 360 μA) to the channels and measured the voltage across the two electrodes. The plot of the measured resistance of the channels versus the effective channel length is shown in Fig. 3(a). It is notable that the measured resistance increased linearly with the effective channel length. Furthermore, the slope of the Rmeas vs. Lch plot was consistent for the different constant currents. The slope of the linear fit was 181.1 ± 2.4 Ω/mm. This means that any increase in Rmeas was only the result of an increase in Lch without effects of the Lch-dependence of Rint. Thus, the conductivity of the PBS solution can be calculated from the slope of a Rmeas vs. Lch plot and Eq. (3). Fig. 3(b) shows the calculated conductivity of the measured PBS solutions. The calculated conductivity was very consistent for the different currents. The conductivity value evaluated by this method was 15.16 ± 0.19 mS/cm. This value fell within the PBS conductivity range reported by other research (15–17 mS/cm), indicating the measured conductivity was a reasonable value [43–46]. To compare the measured conductivity of the PBS solution with the result from commercialized conductivity-measurement equipment. We measured the conductivity of the same PBS solution using electrochemical impedance spectroscopy (EIS). The PBS conductivity conductivity measured from EIS was 15.54 ± 0.60 mS/cm. This result also indicated that the PBS conductivity measured by our method was a reasonable value. More detail investigation of accuracy of the DC-based conductivity-measurement will be discussed in this section by measuring various electrolyte solutions including conductivity standard solutions and comparing EIS results. In contrast to the results using a constant voltage source [Fig. 2(a)], the results using a constant current source indicate that Rmeas vs. Lch is

linear and ΔRmeas/ΔLch is independent of the applied current [Fig. 3(a)]. This implies that the interface resistance is not dependent on the channel length although it may be dependent on the current. Fig. 3(c) shows the plot of the interface resistance as a function of the effective channel length under different currents. The interface resistance for each channel was calculated from the measured resistance and calculated conductivity value at each current condition. The average interface resistance of all channels corresponds to the y-intercept of the linear fit in Fig. 3(a). The results show that the interface resistance was not changed by the effective channel length at the same applied current. Fig. 3(d) presents the plot of the interface resistance as a function of the applied current. The interface resistance decreases with increasing current level because increased current reduces the interface voltage, thereby decreasing the interface resistance. These results prove that liquid conductivity can be evaluated by a multi-channel chip and DC measurement. The effects of interface resistance, which have been a major problem in DC-based liquid measurement, were able to be removed using the proposed method. However, another concern with the measurement of resistance using a DC signal is the effect of electrolysis in liquid. If there is a change in ion concentration due to electrolysis, the conductivity of the liquid may change over time. We thus investigated the time dependence of liquid conductivity determined by our DC measurement method in order to check whether the effect of electrolysis may affect the measured results. We measured the voltage of the channels filled with a 0.1 M KCl aqueous solution by applying a constant current. Fig. 3(e) shows the plot of the measured voltage versus time when applying a constant current of 280 μA to each channel for 60 s. The resistance of the KCl channel is proportional to the measured voltage. The plot shows that the voltage (i.e. the resistance of the channel) increases right after applying the constant current (at t < 10 s) and then saturates. The measured voltage changed less than 1.5% over a 50-s period (10 < t < 60 s) at 10 s after applying the current, as shown in Fig. 3(e). This result indicates that 6

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Fig. 3. (a) The measured resistance of the channels versus the effective channel length under various DC constant currents (200, 240, 280, 320, and 360 μA). The measured resistance increased linearly with the effective channel length. (b) The calculated conductivity of the measured PBS solution. The calculated conductivity is considerably consistent at the various current conditions. (c) The interface resistance as a function of the effective channel length under different currents. The interface resistance was not changed by the effective channel length at the same applied currents. (d) The interface resistance as a function of the applied current. The interface resistance decreases with increasing current level because increased current reduces the interface voltage, thereby decreasing the interface resistance. (e) The measured voltage versus time when applying constant current of 280 μA to each channel filled up with KCl 0.1 M aqueous solution for 60 s. (f) The calculated conductivity as a function of time and relative deviation of the calculated conductivity from the value at 10 s. The difference of the calculated conductivity is observed to be less than 1% over time based on the value at 10 s.

Table 1 The results of the conductivity determined by the proposed method and the EIS. Measured standard solution

Proposed method

EIS

Concentration

Reference conductivity @ 25℃ [mS/cm]

Measured conductivity [mS/cm]

Difference

Measured conductivity [mS/cm]

Difference

KCl 0.01 M KCl 0.1 M KCl 1 M

1.41 12.88 111.8

1.44 ± 0.01 13.19 ± 0.05 110.96 ± 4.90

2.16% 2.42% −0.75%

1.37 ± 0.02 12.62 ± 0.19 97.90 ± 3.79

−3.13% −2.03% −12.43%

any change of liquid resistance under applied DC voltage (or current) may be ignorable if the measurement is done at a short time (˜ 10 s) in a moderate voltage (or current) range. We then calculated the conductivity of the KCl solution based on the measured resistance and the method proposed in this study. Fig. 3(f) shows the calculated conductivity as a function of time (σ(t)) and the change in the calculated conductivity [(σ(t) - σ(t = 10)) / σ(t = 10)]. The difference in the calculated conductivity over time compared with the conductivity at 10 s (σ(t = 10)) was observed to be less than 1%. These results indicate that the effect of electrolysis was negligible when the conductivity was evaluated by the proposed method with the

measurement conditions (current levels and measurement time). The change in conductivity over time for different current levels (200 and 360 μA) is shown in Fig. S2. To ensure stable evaluation of conductivity in this study, the resistance of all liquid channels was measured at 10 s after the constant current was applied to the channel. To verify the accuracy of the liquid conductivity determined using the proposed method, we compared its results with the conductivity of various solutions measured using EIS. For this, we tested standard solutions whose conductivities are known: aqueous solutions of 0.01 M KCl (reference conductivity = 1.41 mS/cm at 25 ℃), 0.1 M KCl (12.88 mS/cm at 25 ℃), and 1 M KCl (111.8 mS/cm at 25 ℃). The 7

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conductivity calculated from the measured resistance is lower than the actual liquid conductivity. In the proposed method, however, the liquid conductivity is evaluated from the difference in channel resistance between channels of different length [ΔRmeas/ΔLch = ΔRch/ΔLch = 1/ (σ∙A)], not from the measured resistance. Because the values of the external resistances are the same in different-length channels, the proposed method can remove the effects of external resistances from the calculation of the difference in channel resistance between channels of different length [ΔRmeas/ΔLch]. Therefore, we can expect that the errors caused by the external resistances are ignorable in the proposed method. In case of EIS, the calculated cell constant can be dependent on the resistance of the conductivity standard solutions by the effect of the external resistances. For example, we determined the cell constants from the EIS results of KCl solutions (0.01 M, 0.1 M, and 1 M) as 1.033, 1.021, and 1.144 cm−1. The appropriate cell constant needs to be selected to precisely determine the conductivity of a specific liquid [48]. We also determined the conductivity of PBS and various types of cell culture media (MEM, DMEM, and RPMI-1640) using the proposed method and EIS. The solutions were tested five times, and the cell constant used for EIS was 1.021 cm−1 which is calculated from the conductivity of 0.1 M KCl solution [48]. The comparison results of the conductivity determined by the proposed method and that from EIS are summarized in Table 2, and the plot of the measured conductivities for PBS and cell culture media are shown in Fig. S3(b) and S3(c). As shown in Table 2, the conductivities evaluated by the proposed method had a small difference (< 3%) from the conductivities measured by EIS. In addition, it was verified that the evaluated conductivity values by the proposed method are consistent for the different constant currents in

Table 2 The conductivity of PBS and various cell culture media determined by the proposed method and EIS. Measured solution

PBS MEM DMEM RPMI-1640

Measured conductivity [mS/cm] Proposed method (A)

EIS (B)

15.15 14.22 14.76 13.11

15.54 14.30 14.92 13.31

± ± ± ±

0.28 0.06 0.39 0.11

± ± ± ±

Difference ((A-B)/B [%]) 0.60 0.48 0.57 0.47

−2.50 −0.53 −1.10 −1.52

conductivity results of the conductivity evaluated by using the proposed method and EIS are summarized in Table 1. The plot of the measured conductivities for KCl with difference concentrations are shown in Fig. S3(a). The conductivities evaluated by proposed method had a small difference (< 3%) from the known reference values, thus confirming that the conductivity of standard solutions can be accurately measured with the proposed method. The conductivities of the 0.01 M and 0.1 M KCl solutions calculated by EIS also had a small difference (< 4%) from the known reference values. However, the conductivity of 1 M KCl solution calculated by EIS had a difference larger than 10%. These results imply that measurement of a liquid with low resistance may cause errors in determining the conductivity of a liquid. The measured liquid resistance may be larger than actual liquid resistance because this includes not only liquid resistance but also external resistances, such as wire resistance, electrode resistance, output resistance of power source, and input resistance of measurement instrument. This means that the

Fig. 4. (a) The measurement process of electrophoretic velocity of charged nanoparticles with an average diameter of 110 nm in PBS for zeta-potential analysis (upper left) and fluorescent image of the nanoparticles (upper right). When the electric field is applied to the suspension, the charged nanoparticles drift in the opposite direction of the electric field because the charged nanoparticles are negatively charged. (b), (c) The results of zeta-potential analysis of charged nanoparticles under various DC constant currents (100, 140, and 200 μA). 8

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Fig. S3(b) and S3(c). From these results, it was confirmed that the conductivity of various solutions could be accurately determined from the proposed method without calibration by the conductivity standard solution.

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3.4. Evaluation of nanoparticle zeta potential using the proposed conductivity evaluation method As mentioned in Section 2.5, the conductivity of a liquid is important in the zeta-potential analysis of charged nanoparticles. The zeta potential of nanoparticles is determined by the electrophoretic velocity of the nanoparticles and the electric field applied to the nanoparticles. Fig. 4(a) presents the measurement process for electrophoretic velocity. We applied various constant currents (100, 140, and 200 μA) to the channels filled with PBS and nanoparticles. Because the nanoparticles are negatively charged, these nanoparticles drift in the opposite direction to the electric field. The electrophoretic velocity is the drift distance per unit time. Based on the conductivity of PBS determined by using the proposed method, the electric field was calculated at the various constant currents (100, 140, and 200 μA) as 19.35, 27.09, and 38.70 V/m. We analyzed the zeta potential of the nanoparticles based on Eq. (2). Fig. 4(b) and (c) present the results for the zeta-potential analysis. The number of nanoparticles used to the zeta-potential analysis was 208, and the average zeta potential for constant current conditions of 100, 140, and 200 μA was −53.9, −52.3, and −54.7 mV, respectively. These values are comparable to the zeta potentials reported in previous studies [49,50]. In addition, the distribution of zeta potentials for these nanoparticles was similar to a Gaussian distribution, as shown in Fig. 4(c). From these results, we verified that the zeta potential of nanoparticles can be analyzed using the liquid conductivity which is evaluated from the method proposed in this study. 4. Conclusion In this work, we designed and fabricated a multi-channel microfluidic chip that had multiple liquid channels with varying channel lengths and an identical electrode structure. We also developed a measurement and analysis method for the evaluation of liquid conductivity. We evaluated the precise conductivity of a liquid using a simple DC measurement approach. We confirmed that the accuracy of the proposed method by using a conductivity standard solution whose conductivity is known. We also measured the conductivity of the same solutions using EIS equipment and compared the EIS results with those obtained from the proposed method. The results of time-dependence testing indicated that the effect of electrolysis was negligible when the conductivity was evaluated by the proposed method. The liquid conductivity can be evaluated by the proposed method with a small amount of liquid (< 1 ml). This means that the proposed method may be applied to the evaluation of the conductivity of a biological solution whose volume is not enough for the conventional EIS. This method also can be used for analysis of the electrochemical properties of liquid-electrode interface. Acknowledgements This work was supported in part by the Bio & Medical Technology Development Program of the National Research Foundation (NRF) funded by the Ministry of Science & ICT (2017M3A9G8083382) and the NRF grant funded by the Korea government (MSIT) (2017R1A4A1015565). Appendix A. Supplementary data Supplementary material related to this article can be found, in the 9

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