Electric current generation and critical micelle concentration (CMC)

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Surfaces, Interfaces, and Applications

Coalescence of a water drop with an air-liquid interface: Electric current generation and critical micelle concentration (CMC) sensing application Yongxin Song, BIN XU, Yapeng Yuan, Hao Xu, and Dongqing Li ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b00365 • Publication Date (Web): 01 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019

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ACS Applied Materials & Interfaces

Coalescence of a Water Drop with an Air-Liquid Interface: Electric Current Generation and Critical Micelle Concentration (CMC) Sensing Application

Yongxin Song1, Bin Xu1,+, Yapeng Yuan1,+, Hao Xu1 and Dongqing Li*2

1 Department of Marine Engineering, Dalian Maritime University, Dalian, 116026, China 2 Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo , ON, N2L 3G1, Canada

*Corresponding author: E-mail: [email protected] +

Bin Xu and Yapeng Yuan contributed equally to this work.

1

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ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract A phenomenon that an electric current is generated when a pedant water droplet touches an air-electrolyte solution interface is investigated in this paper. A measurement system developed in this study consists of a hollow electrode for droplet generation, a counter electrode immersed in an electrolyte solution and an electrometer with high precision. Once a droplet touches the air-electrolyte solution interface, it will be pulled into the electrolyte solution and an electric current is produced during this process. Experiments show that the magnitude of the electric current depends only on the pedant droplet and has nothing to do with the types of the electrolyte solution (with a much larger volume than that of the droplet) below the drop. The electric current is generated by the electric potential difference between the droplet and air-electrolyte solution interface and the liquid bridge formed during the droplet coalesce. As a result, the magnitude of generated electrical current mainly depends on the size, the pH and the type of the solution forming the droplet. Determining the critical micelle concentration (CMC) using this system was successfully achieved to show the powerfulness of this system.

Keywords: electric current; pendant droplet coalescence; air-liquid interface; liquid bridge; surface charge detection

2


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1. Introduction It is well-known that there are electrical charges at the solid-liquid and liquid-fluid interfaces.1,2 These surface charges are important in controlling the physical and chemical behavior of the droplets. Ever since Rayleigh’s pioneer study,3 extensive studies have been conducted and the continually improving understanding of the electrical phenomena at interfaces results in wide applications in the fields of colloid stability,4-7 electrostatic spraying,8-13 digital microfluidics and nanofluidics,14-18 droplet-based microreactor,19-21 energy harvesting22-30 and so on. Among the various kinds of interface electrical phenomena, the electrical property of a water droplet in air has gained many interests. Lord Kelvin designed the well-known “Kelvin water dropper” to demonstrate the present of free charge in droplets falling from a faucet.31 This system works by letting water droplets detach from a metal faucet under gravity and pass through a metallic ring. The charges on the droplet surface can be evidenced by the voltage difference between two buckets. Based on this phenomenon, applications such as generating charged water droplet at a very high speed,32 harvesting energies with a high conversion efficiency,33,34 and producing a dual spray ionization source for mass spectrometry

35

have

been successfully demonstrated. Typically, charged liquid droplets can be generated by using a biased high voltage.36 Recently, charging water droplets with a solid insulator has received much attention due to its potential for energy harvesting.22-30This process generally involves a water droplet touching and then removing from the solid insulator. When the droplet contacts the solid material, both the water droplet and the solid material will be charged due to the contact-electrification effect22-26 or charge separation effect.27-30 An electric double layer capacitor at the solid-liquid interface will be formed when the droplet contacts the solid. There are charges stored in this capacitor and this process can be considered as a charging process. When the droplet removes from the solid, some charges in the diffuser layer of the EDL will be sheared to the droplet and correspondingly, a charge induction process will occur. By designing a proper electrical circuit, the electrical energy can be collected. More details about using a 3



water droplet to harvest energy can be found in a recently published review paper37. Charging a water droplet with a charged solid by employing the so-called contact electrification effect was also reported.38 In essence, the above-mentioned phenomena reflect the charge induction principle, i.e., a charged droplet, no matter how it is charged, induces charges by passing through a metal ring or by touching an insulator or by touching a charged solid. Theoretically, charge induction principle also works for a charged droplet detaching directly from a metal material. As reviewed above, for generating an electrical current with a charged water droplet, the approach of using the charge induction principle was applied. This paper reports a new method of generating electrical current by letting a pendant water droplet in air touch an air-electrolyte solution interface. An experimental system developed in this study includes a hollow electrode for droplet generation, a counter electrode immersed in an electrolyte solution and an electrometer with high precision. Once a droplet touches the air-electrolyte solution interface, it will be pulled into the electrolyte solution and electric current is generated during this process. The factors that influence the magnitude and the direction of the detected current were analyzed and experimentally verified. Measuring the CMC value of ionic surfactant using this system was also demonstrated. It should be emphasized that the working principle of this new system presented in this paper is different with the above reported investigations. Furthermore, the focus of this paper is the generated electric current during the coalescence of a droplet with a flat liquid-air interface which is less investigated. 2. Experiments 2.1 Experimental system Figure 1 shows the droplet-coalescence electrical current generating system which consists of a hollow stainless steel electrode grade UNS304 (named as droplet electrode), a counter electrode immersed in an electrolyte solution, an electrometer (6517B, Keithley, USA) and a computer to show the data measured by the electrometer (Figure 1(a)). The droplet electrode is connected with a soft tube to a water container. A mini valve was used to control the continual generation of water droplets. The current measured by the electrometer was shown and stored in the computer simultaneously. The measurement starts by growing a droplet 4


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from the hollow electrode (with a distance of h from the electrolyte surface). Figure 1(b) illustrates the process of the formation and growth of the droplet. As the droplet grows, it gradually approaches the air-electrolyte solution interface below the droplet. Once the droplet touches the interface, it will be pulled into the bulk liquid instantly. Negative probe Electrometer

A Positive probe

Valve Droplet electrode Counter electrode

h Electrolyte (a)

Droplet electro de

Q0=0

Q1 = S1.

Q1 = S2 .

Air Electrolyte solution

(b)

Figure 1 The experimental system setup (a) and droplet charging by continually increasing its surface area (b) (Q is the surface charges of the droplet, S and  are the surface area and surface charge density of the droplet, respectively.) 2.2 Liquid solution preparation and experimental procedure In this study, pure water, NaCl solutions with different pH values and ionic surfactant (SDS or CTAB) solutions were employed to test the charge transfer phenomenon. The pure water was produced by a Millipore system (Milli-Q synthesis, Millipore, USA). The procedures for preparing the NaCl solutions and ionic surfactant solutions can be found in the two reference papers39,40 respectively. 5



Experiments were carried out by loading 50 mL electrolyte solution into a glass beaker first at room temperature (22±1℃). Then the distance between the droplet electrode tip (made of stainless steel with an inner diameter of 1.3mm and an outer diameter of 1.6mm) and the air-electrolyte solution interface, h was adjusted to a predetermined value as shown in Table 1. After the valve below the solution container was opened, a droplet was formed at the tip of the droplet electrode and gradually grew larger until the droplet touched the air-electrolyte solution interface, as shown in Figure 2. At last, the droplet was pulled into the bulk electrolyte solution. During this process, the electrical current was measured by an electrometer (6517B, Keithley,USA). Afterwards, a new droplet was formed and grew gradually. The process repeats. For each experiment, at least five current signals were measured repeatedly and an averaged value was obtained and used to plot the curves. 3. Results 3.1 Detecting the electric current Figure 2 shows the typical results of the measured electric current when a pure water droplet touches an air-pure water interface (h = 1.5mm). As is shown in Figure 2, in terms of the electric current, each droplet can generate a downward pulse with a magnitude of about 63.7nA and according to the instruction manual of the electrometer, the downward current pulse means that the current flows from the droplet electrode to the counter electrode immersed in the electrolyte. From the amplified signal, we can also find that the time-duration of the signal with the largest magnitude is about 0.1s. The time duration between point a and b is about 20ms, meaning that the frequency is 50Hz. Since the sampling frequency of the electrometer is as high as 400 per second, this means that 400 points will be sampled per second. For digital sampling, it is widely accepted that the sampling rate should be at least double the highest frequency of the detected signal. It’s clear that the sampling frequency of the electrometer is high enough. For time-duration of the signal with the largest magnitude, it is about 0.1s, meaning that 40 points per second can be sampled which is enough to determine the largest signal magnitude accurately. 6


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0

Current (nA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a

-20 -40 -60

b 0.1s 0

100

200

300

400

500

Time (s)

Figure 2 Measured electrical current when a pure water droplet touches the air-pure water interface (h=1.5mm, a is the pulse starting point, b is the pulse peak point) For such an experiment, it is important to know when exactly the current was generated. To do so, the current signals and potential difference between the droplet and the counter electrodes (measured with an oscilloscope (DS1052E, RIGOL, China)) during the falling of the droplet (h = 1.5mm) were observed at the same time with a microscope (SMZ1270, Nikon, Japan). It was found that the current was generated at the critical moment when the droplet touches the electrolyte solution, as is indicated by the red circle in Figure 3. After that moment, the current returns to the baseline even when the droplet still contacts the liquid surface. Theoretically, the current flowing through the electrometer should be generated by an electrical potential difference which exists when the droplet touches the electrolyte solution. To determine the electrical potential, the potential difference between a pure water droplet and the pure water solution was measured by an oscilloscope with a sampling frequency of 50 MHz (Supporting Information and Figure S1).

Water droplet Air

Generated at the moment of touching

Pure water

Figure 3 The critical moment of generating an electric current 7



Figure 4 shows the measured results. From Figure 4, it’s clear that an upward potential pulse with a magnitude of about 43mV was generated. It was observed that the ‘increasing stage’ of the pulse is generated during the growth of the droplet. A ‘decreasing stage’ is the process of the droplet merging into the electrolyte solution. The joint point of the two stages, i.e., the peak point of the signal is the critical moment of the droplet touching the electrolyte interface. This means that the electric potential difference of the droplet electrode is positive (relative to that of the counter electrode in the solution). Therefore, the direction of the electric current 0.10

should be from the droplet electrode to the counter electrode. This result agrees well with the 0.09

direction of the current measured by the electrometer. 0.08 80 0.07

60 0.06 0.05

ΔV

U/mV Voltage (mV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.04 40

Decreasing stage

Increasing stage

0.03

20 0.02 0 -0.15

20 -0.10

40 -0.05

60 0.00

80 0.05

100 0.10

120 0.15

T/ms Time (ms)

Figure 4 Evolution of potential difference (ΔV) between the droplet and the electrolyte solution with time 3.2 The sign of the surface charges of the droplet Due to the very complex charging mechanism, a pedant water droplet can be either positively or negatively charged. Therefore, one of the most fundamental issues for this system is to determine the surface charge polarity of the droplet. In this study, the deformation of the droplet and the electrolyte surface when they were separated with a sufficient small distance was used to evaluate the surface charge polarity of the droplet, according to electrostatic interaction of two charged surfaces. The approaching a water droplet released from the droplet electrode to a pure water-air interface was recorded with a high-speed camera (Phantom v2012, VRI, US) with a sampling frequency of 100 fps and shown in Figure 5. 8


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As is shown in Figure 5 (a), as the pure water droplet approaches the electrolyte surface, the tip of the droplet still keep it original shape. However, right below the apex of the droplet, there is a flat shadow region appeared at the air-electrolyte interface. This means that the two surfaces are electrostatically repulsive to each other. Since it is well-known that the pure water-air interface is negatively charged, the pedant droplet of pure water generated from the droplet electrode should also be negatively charged. To verify the above analysis, the deformation of a droplet of the surfactant CTAB solution (0.82mM) and the air-pure water interface was recorded too (Figure 5 (b)). From Figure 5 (b), it’s obvious that the droplet is slightly elongated at its apex. As regards to the air-pure water interface, there is also a convex region underneath that of the droplet. These deformations clearly demonstrated that the droplet and the air-pure water interface are attracted to each other. This is because the CTAB is a positively charged surfactant; the droplet of the CTAB solution has positive surface charges which will attract the negative surface charges at the air-pure water interface. Based on the results shown in Figure 5, it’s clear that the pedant droplet of pure water has negative surface charges. This also excludes the possibility of generating a transient streaming current when the liquid flows through the droplet electrode, which would require the pure water droplet to have positive surface charges.

9



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300μm

(a)

300μm

(b) Figure 5 Surface deformations before the droplet touches the pure water solution, (a) pure water droplet, (b) CTAB droplet To clearly understand the current generation mechanism, factors such as the surface charges of the droplet and the types of the water solution will be investigated in the following sections. 3.3 Dependence of the electrical current on the surface charges of a droplet Theoretically, the negative surface charges the water droplet bears are determined by the size and surface charge density of the droplet:41

 =

Q 40 r a

=

 a  0 r

(1)

where  is the zeta potential of the droplet surface, Q is the total amount of charge on the droplet,  is the surface charge density, a is the radius of the droplet, ε0 is the permittivity of 10


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vacuum and εr is the relative permittivity of the droplet. Based on Eq. (1), it’s clear that for the same type of droplet, the amount of surface charges is proportional to its surface area. On the other hand, for a certain size of droplet (a is constant), the amount of surface charges is proportional to its zeta potential. In this section, both the surface area and zeta potential effects on the measured electrical current will be presented. 1) surface area effect To study the effect of the surface area, the height (h in Figure 1) between the tip of the droplet electrode and the horizontal air-water interface was adjusted to different values. The generated electric currents were then measured under different h.

Figure 6 shows the shapes

of the droplets at the critical moment of just-before-touching the horizontal air-water interface as recorded with a microscope imaging system (SMZ1270, Nikon, Japan). It’s clear that the droplet becomes ellipsoidal with the increase in h. The droplet is elongated by the balanced force between the continually increased gravity force and the surface tension between the electrode and the droplet. The surface area of the droplets exposing to air (from the tip of the droplet electrode (indicated by the red dash line in Figure 6) to the apex of the droplet) becomes larger with the increase in h. Once touching the electrolyte solution, the force balance is destroyed and the droplet will be pulled into the electrolyte solution.

11



500μm

(a)

500μm

(b)

500μm

(c)

500μm

(d)

12


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500μm

(e) Figure 6 The shapes of the droplets at the critical moment of touching the air-electrolyte interface, (a) h=1.5mm；(b) h=2.0mm；(c) h=2.5mm；(d) h=3.0mm； (e) h=3.5mm To accurately calculate the surface area of the droplets before detached from the electrode, the pictures shown on the left hand side of Figure 6 were digitized with Solidworks and shown on the right hand side of Figure 6. The surface areas of the digitized droplets were then calculated and shown in Table 1. Table 1 Dependence of the surface area of the droplets on h h（mm）

Surface area（mm2）

1.5

9.78

2.0

14.78

2.5

20.34

3.0

26.89

3.5

33.13

Figure 7 shows the dependence of the magnitude of the measured current on the surface area of the droplet. Each data point shown in Figure 7 is the average value of at least five signal pulses. From Figure 7, we can clearly see that the measured current has a linear relationship with the surface area of the droplet, with a correlation coefficient (R2) of as high as 0.9898. The linear relationship is as the following: I output = −3.84  S − 27 .23

Recalling that the amount of surface charges is linearly proportional to its surface area (Eq.

(2)

13



(1)), such a linear relationship predicted by Eq.(2) means that the generated electric current is linearly proportional to the amount of the surface charges of the droplet.

Experimental data Linear fit

-60

Measured signal (nA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-80

-100

-120

-140

-160

-180 10

15

20

25

30

35

Surface area of the droplet (mm2)

Figure 7 Dependence of the magnitude of the measured current on the surface area 2) Zeta potential effect Generally, for a given ionic concentration, the zeta potential is a function of the pH value.42,43 Therefore, it is expected that the droplets with different pH values will generate current signals with different magnitudes. To verify this, in this study, the currents generated by 0.1M NaCl droplets with different pH values, i.e., different surface charge densities were measured and the typical signals are shown in Figure 8. The zeta potential values for 0.1M NaCl solutions under different pH values are given by a published paper.44 The dependence of the measured current on the zeta potentials of the NaCl droplets is summarized in Table 2 and also plotted in Figure 9. From Figure 8, it is clear that NaCl droplets also generate downward signals whose magnitudes increase linearly with the increase in the pH values or the zeta potentials. As shown in Figure 9, the linear correlation between the generated electric current signals and the zeta potentials (correlation coefficient R2=0.9893) is given by: I output = 15 .74   − 35 .71

where  is zeta potential of the air-NaCl droplet interface(mV). 14


(3)

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Such a linear relationship between an electrical potential and the resulted electric current is helpful in formulating the underlying mechanism of current generating by the droplet touching an electrolyte solution.

Current (nA)

0 -50 -100 -150 -200 0

100

200

300

400

500

300

400

500

300

400

500

Time (s)

(a)

Current (nA)

0 -60 -120 -180 -240 0

100

200

Time (s)

(b) 0

Current (nA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-80 -160 -240 -320 0

100

200

Time (s)

(c)

15


0.1s


Current (nA)

0 -100 -200 -300 -400 0

100

200

300

400

300

400

500

Time (s)

(d) 0

Current (nA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-100 -200 -300 -400 0

100

200

500

Time (s)

(e) Figure 8 Typical signals generated by NaCl droplets with different pH values (h=1.5mm). (a) pH=2, (b) pH=4, (c) pH=5, (d) pH=5.5 and (e) pH=8 Table 2 Measured current with NaCl droplets under different pH values and the same ionic concentration (0.1M). The zeta potential values are taken from reference.45 Zeta potential

Measured current

(mV)

(nA)

2

-9

-186.69

6.36

4

-12

-230.10

6.26

5

-17

-300.18

3.71

5.5

-20

-352.24

7

8

-19.7

-350.72

4.83

pH

SD

16


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-150

Experimental data Linear fit -200

Measured signal(nA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-250

-300

-350

-20

-18

-16

-14

-12

-10

-8

Zeta potential(mV)

Figure 9 Dependence of the magnitude of the measured current on zeta potentials of the NaCl droplets of the same concentration 3.4 Electrical current by different air-liquid interfaces To fully understand the current generating mechanism, it is greatly desired to study the electrical current generated by different air-liquid interfaces. Table 3 shows the measurement results by a pure water droplet touching different air-liquid interfaces, using the system shown in Figure 1 (h=1.5mm). The details about surfactant solution preparations can be found in the ‘Materials and experimental procedures’ in the Supporting Information file. It’s clear that there is no obvious difference for the averaged current by a pure water droplet touching different air-liquid interfaces. Table 3 Electrical current generated by different air-liquid interfaces Air-liquid interface

Averaged current (nA)

SD

Air-pure water

62.66

1.8489

Air-1% NaCl solution

62.34

1.3718

Air-2% NaCl solution

63.03

1.4475

Air-3.5% NaCl solution

62.58

1.5043

Air-6.94 mM SDS solution

64.37

1.6204

Air-0.82mM CTAB solution

64.19

1.7606

17



4. Discussions Based on the above results, the mechanism of the current generation by the coalesce of a droplet with a surface of a bulk liquid can be reasonably explained by Figure 10 which shows the

equivalent circuits before and when the droplet touches the air-liquid interface.

Droplet electrode

A

Counter electrode

CEDL,1

CEDL,2 Rd

Rs

(a)

Droplet electrode

A

Counter electrode

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CEDL,1 CEDL,2 Rd Rb

Rs

(b) Figure 10 Equivalent circuits before (a) and after (b) the droplet touches the electrolyte solution 1) Before the droplet touches the air-liquid interface (Figure 10 (a)) The system before the droplet touches the air-liquid interface can be electrically modeled as the connects of two resistors (named as Rs for the liquid solution and Rd for the droplet) and 18


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two capacitors (shown in Figure 10): the EDL capacitor of the droplet electrode-electrolyte solution interface (named as CEDL,1), the EDL capacitor of the counter electrode-electrolyte solution interface (named as CEDL,2). The capacitance of an EDL capacitor is given by: CEDL =

 0 l q =  

(4)

where q and  are the charge density and zeta potential of the EDL respectively, ε0 is the dielectric constant of vacuum and εl is the relative dielectric constant of the electrolyte solution,  is the thickness of the EDL. (1) Capacitor CEDL,1 This is the EDL capacitor formed by the inner surface of the hollow electrode filled with the electrolyte solution. For this electrode, it always contacts an electrolyte solution in order to continually generate the droplet. Therefore, both the zeta potential and the contact area will not be changed during the merging process of the droplet. That is to say, this capacitor does not make contribution to the detected current. (2) Capacitor CEDL,2 This is the capacitor formed between the counter electrode and the liquid in the container. For this electrode-liquid interface, the electric double layer is always the same because of the constant contact area with the liquid and the same type of the liquid and electrode and thus the same zeta potential. Furthermore, the contact area can hardly be changed by the merging of the droplet since the volume of the bulk liquid is much larger than that of the droplet. Accordingly, there is no reorganization of the EDL at this electrode during the droplet merging process. Similar to CEDL,1, this capacitor does not make contribution to the detected current. As is shown in Figure 10 (a), the whole system is electrically open before the droplet touches the air-liquid interface and thus there will no current detected. 2) When the droplet touches the air-liquid interface (Figure 11(b))

It is well known that an air-electrolyte interface (either the water droplet in air or the bulk electrolyte solution in this system) has surface charges, which is mainly due to the 19



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spontaneous adsorption of specific ions.46,47 For a pure water droplet in air, it has negative surface charges.48-50 This can be attributed to the fact that the cations are prone to be hydrated and hence like to stay in the bulk water, while the anions are likely to accumulate at the surface.51

Due to the presence of the surface charges, the droplet surface has an electrical potential (Vdroplet) which generally is not measureable. In the field of electrokinetics, it has been widely accepted to use the measurable zeta potential (  ) of the electric double layer (EDL) to approximate this surface electric potential.41,42

Vdroplet =  =

Q 40 r a

=

 a  0 r

(5)

where Q is the total amount of charge on the droplet,  is the surface charge density, a is the radius of the droplet, ε0 is the permittivity of vacuum and εr is the relative permittivity of the droplet. From Eq. (5), it’s obvious that electrical potential increases with the increase in the size of the droplet (diameter a) and the surface charge density (). For a flat air-liquid interface, the relationship between the surface charge density and zeta potential is given by44

0 =

 ' k kbT 2n ( ze)2

= Vbulk surface

(6)

where k is the Debye-Huckel parameter, ’ is the surface charge density, kb is the Boltzmann constant, T is the absolute temperature, e is the charge of a proton, z and n∞ are the valence and bulk ionic concentration of the ion respectively. Therefore, the potential difference between the droplet and the flat air-liquid interface is:

V = Vdroplet − Vbulk surface

(7)

The coalescence of the droplet with the liquid interface is started by forming a liquid bridge52. This process can be modeled as the forming of a new resistor (Rb in Figure 10 (b)). With the potential difference across the liquid bridge (Eq.(7)), there will be an electrical current flowing from the droplet to the solution, according to the ohm's law: 20


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I=

V Rb

(8)

One thing to be noted that the above two equations are from the classical EDL theory, under the assumption of constant surface potential or constant surface charge density and without any interaction with external electric field. However, for liquid-fluid interface, the surface charges are mobile.53 When the charged droplet approaches to the air-fluid interfaces to a sufficiently close distance, there are electrostatic interactions between the two charged interfaces. In this study, the droplet is pure water, the bulk liquid below it is an electrolyte solution. Generally, the pure water droplet has a higher surface charge density or a higher zeta potential, and the air-electrolyte solution interface has a lower surface charge density or a lower zeta potential. The stronger electric potential from the surface of the droplet apex pushes away the mobile surface charges at the air-electrolyte solution interface right below the droplet apex; so that the local surface charge density of the air-electrolyte solution interface immediately below the droplet apex is changing dynamically. As a result, the potential difference between the droplet and the air-liquid interface surface is changing too, as is clearly evidenced by the ‘increasing stage’ shown in Figure 4. Such an electrostatic interaction determines the electric potential difference right before the droplet contacts the air-electrolyte solution interface and reaches a value that is mainly determined by the electric potential of the droplet surface. In this way, no matter the ionic concentration and the type of the electrolyte in the bulk electrolyte solution, the electric potential difference right before the droplet contacts the air-solution interface, and hence the generated electric current, is independent of the properties of the bulk solution (as is clearly shown in Table 3). By combining Eq. (5)-(7), Eq.(8) can be re-written as:

I=

 a  0 r Rb

(9)

In addition, it should be noted that, upon coalescence, the hydraulic pressure at the droplet side is higher and therefore the flow in the liquid bridge is from the droplet to the bulk liquid solution. 54 In other words, the liquid of the bridge is the liquid of the droplet. As a result, the electric 21



resistance of the liquid bridge is mainly determined by the droplet. Obviously, based on Eq. (9), the measured current will be dependent on the diameter and surface charge density (related with zeta potential) of the droplet. More specifically, larger droplets with higher zeta potential will result in larger electrical current through the system. The value of Rb can be estimated by using

Eq.(9) once the current (I), the surface charge density () and the radius of the droplet (a) are known. With the very quick coalescence between the droplet and the air-solution interface, the potential difference will disappear quickly (as the “the decreasing stage” shown in Figure 4) and there will be no current in the system. This means that there will be no current even the droplet still contacts both the air-liquid surface, as is experimentally demonstrated in Figure 4. 3) Other discussions As is analyzed above, the capacitors of CEDL,1 and CEDL,2 always exist and will not change during the whole process. In a word, it is the electrical properties of the liquid bridge, e.g., its resistance and electrical potential difference that controls the measured electrical current. Based on this model (Figure 10), we can revisit the experimental results shown in Section 3. As indicated by Eq. (5), increasing either the surface area or the surface charge density of the droplet will increase the magnitude of the detected current. This theoretical prediction agrees well with the experimental results (Figure 7 and Figure 9). As is discussed in Section 4.1, the measured current is mainly generated by the electric potential across the liquid bridge. It is expected that, for droplets of the same size, the measured current should be dependent on the zeta potential of the droplet. This theoretical analysis also agrees well with the experimental results shown in Figure 9. In this system, there are also some other processes involved, such as continually growing the droplet, the approaching to and contacting with the liquid interface. As regards to the droplet growing process, it should be noted that it is the final size of the droplet, not the rate of droplet growth, that affects the magnitude of the detected current. As to the current generation, larger droplet growth rate which results in faster droplet coalesce is favorable. Regarding the contacting state, factors such as the contacting time duration and the contacting 22


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area, they are influenced by the size and approaching speed of the droplet. The contacting state may have influences on the generated current by influencing the shape of the liquid bridge (also Rb). In this paper, the droplet growing speed is controlled to be very slow and always the same. Thus the related side effects can be controlled to be the minimum. 5. Determining the critical micelle concentration Eq. (3) has several important applications on surface charge sensing. For example, the zeta potential or the surface charge density of an un-known droplet can be compared with that of a known droplet (with known zeta potential, or surface charge density) based on Eq.(3) and the pre-determined surface area (S). Furthermore, factors that influence surface charges of a droplet, such as concentrations of ionic surfactants or proteins, constituents or humidity of the air, can also be quantitatively investigated with the relationship between zeta potential and measured current (Eq.(3)). Here measurement the ionic surfactant concentration was taken as a typical example to show the application of this system. Theoretically, increasing ionic surfactant concentration will increase the amount of surface charge, i.e., the magnitude of electrical potential, of the droplet.55 More specifically, the relationship between the magnitude of electric potential and the surfactant concentration can be divided into two stages. The first one is an increasing-stage: the magnitude of the potential is higher with a higher surfactant concentration before CMC. The second one is a no-change stage: the magnitude of the potential does not change beyond the CMC. The intersection point of the above two stages is the CMC.40 As is previously demonstrated, the measured electrical current reflects the electrical potential of a pedant droplet (Eq.(3)). As a demonstration of the typical applications, the measurement of the CMC values by this method was demonstrated in this section. Droplets with different surfactant concentrations were generated to touch an air-pure water interface. More experimental details about this measurement can be found in the Supporting Information and Figure S1. Figure 11 (using the data in Table S1 and Table S2 of the Supporting Information) shows the dependence of measured signals on surfactant concentrations. Two distinct stages can be obviously observed: the first magnitude-increasing stage with the linearly increased electrical 23



potential of the droplet with the log concentration of the solution. Following the first stage is a straight line with zero slope.56,57 Using the curve-fitting-CMC-determining method40, the CMC values was obtained and shown in Table 4. Comparing with the CMC values measured by other methods (also shown in Table 4), one can concluded that this droplet method is reliable and can achieve the same resolution in CMC measurement. R2=0.9632

Signal (V)

-1

-2

-3

9.21mmol/L -4

-5 1

Concentration (mmol/L)

10

(a)

-7.5

R2=0.9746 Signal (V)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

-8.0 -8.5 -9.0

1.04mmol/L

-9.5 -10.0 -10.5 0.1

Concentration (mmol/L)

1

(b) Figure 11 Dependence of the measured signals on the concentration of surfactant in pure water: (a) SDS; (b) CTAB

24


Page 24 of 32

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Table 4 CMC values measured by different methods Methods

SDS（mmol/L）

CTAB（mmol/L）

This study

9.21

1.04

By conductance

8.08[58]

0.97[59]

By Surface tension

8.0[60]

1.0[61]

By Capillary electrophoresis

8.3

0.93

Other methods

8.1-8.4[62,63]

0.90-0.98[62]

6. Conclusions This paper describes an experimental investigation of the charge transfer phenomena when a pendant droplet in air touches an air-electrolyte solution interface. The electrical current was measured with an electrometer when a droplet touches the air-electrolyte interface and fall into the bulk electrolyte solution. It’s experimentally shown that the electric current is generated by the electrical potential difference between the droplet and the air-liquid interface and independent of the types of the electrolyte in the bulk liquid below the droplet. Therefore, the measured current is linearly proportional to the surface area of the droplet. Furthermore, the magnitude of electric current depends on its pH and hence on the zeta potential. The direction of the measured current is from the droplet electrode to the counter electrode as the electric potentials of all droplets tested in this study are positive relative to that of the electrolyte solution. The system presented in this paper has wide applications in studying surface charge related phenomena, zeta potential of a droplet in air, generating electrical current with droplets and droplet-based air quality sensing. Acknowledgment The authors wish to thank the financial support of National Science Foundation program of China (51679023) to Y. Song, the Natural Sciences and Engineering Research Council of Canada through a research grant (RGPIN-03622) to D. Li. The support from Fundamental Research Funds for the Central Universities (3132016325) and from the University 111 project of China under Grant No. B08046 are greatly appreciated.

25



Supporting Information Available: Measuring the electrical potential difference between the droplet and the liquid solution, CMC measurement

26


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31



GRAPHICAL ABSTRACT

Electrometer

I

Counter Electrode

Droplet

Electrolyte droplet Air Electrolyte

Electrolyte 0

Current (nA)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 32

-20 -40 -60 0

100

200

300

Time (s)

32


400

500

Electric current generation and critical micelle concentration (CMC)

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