Impedance spectroscopy interpretation of silica and polystyrene colloidal suspensions

Journal Pre-proof Impedance spectroscopy interpretation of silica and polystyrene colloidal suspensions Bremnen Véliz, Albert Orpella, Manuel Dominguez, Sandra Bermejo PII:

S0254-0584(20)30002-X

DOI:

https://doi.org/10.1016/j.matchemphys.2020.122620

Reference:

MAC 122620

To appear in:

Materials Chemistry and Physics

Received Date: 27 September 2019 Revised Date:

27 November 2019

Accepted Date: 1 January 2020

Please cite this article as: B. Véliz, A. Orpella, M. Dominguez, S. Bermejo, Impedance spectroscopy interpretation of silica and polystyrene colloidal suspensions, Materials Chemistry and Physics (2020), doi: https://doi.org/10.1016/j.matchemphys.2020.122620. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Impedance spectroscopy interpretation of silica and polystyrene colloidal suspensions Bremnen Véliza,b, Albert Orpella a, Manuel Dominguez a, Sandra Bermejo a* a

Polytechnic University of Catalonia, Dept. of Electronic Engineering, MNT Group, Barcelona, Spain Salesian Polytechnic University, Dept. of Electronic Engineering, GISCOR Group, Guayaquil, Ecuador * Corresponding author: UPC, Micro and Nanotechnologies Group, c/. Jordi Girona 1-3, Campus Nord, 08034-Barcelona-Spain. Email-address: [email protected] b

Keywords: polystyrene nanoparticles, silica nanoparticles, colloid, impedance spectroscopy. Abstract— Impedance spectroscopy differences between colloidal 295-nm silica and 300-nm polystyrene nanoparticles in deionized water are analyzed in this work. Using two different two-electrode measurement setups, designed for this application, impedance spectroscopy measurements performed directly in the colloidal suspensions with same nanoparticles size, shape and concentration, are fitted using Randles circuit models. The parameter analysis allows to identify the suspension response, the electrode-suspension interfaces response and nanoparticle double layer response. The first measurement system consists of a two aluminum wire electrodes characterized in a frequency range from 0.1Hz to 100kHz while the second system was two square stainless steel electrodes characterized from 0.1Hz to 5MHz. According to the results, polystyrene nanoparticles suspension presents higher conductivity and higher values of capacitance than silica suspension. It is revealed that as the nanoparticle concentration decreases, the suspension conductivity decreases for both colloidal suspensions. On the other hand, the electrode polarization effect contributed with high impedance and capacitance values, but showed a contrary behavior with the variation of the nanoparticles concentration. These differences found mainly arise because of the hydrophilic and hydrophobic nature of the silica and polystyrene nanoparticle surfaces.

1.

Introduction

Colloidal nanoparticles are non-agglomerated solid nanoparticles suspended in an aqueous medium. The advances in the synthesis and manipulation of colloidal nanoparticles have produced a huge variety of uses and potential applications for this type of systems. For instance, silica nanoparticles are widely used in the food industry as anticaking additives to improve the taste value and prolong the shelf-life of food [1]. The spontaneous motion of colloidal nanoparticles have allowed the self-assembly of 3D ordered nanostructures for phonic application such as photonic crystals [2] [3], inverse opals [4] or 2D nanostructures as plasmonic colloidal films [5] [6]. In our case, the use of dielectrophoretic force [7] over colloidal suspensions in water have been ideals to build nanostructures by Electrospray

1

[8] [9], such as novel types of metal-insulator-metal capacitor structures with silica nanoparticles [10] [11] or polystyrene nanoparticles [12] as the insular layer.

On the other hand, impedance spectroscopy [13] is a no-destructive tool commonly used to analyze the conductivity properties of liquids, therefore it also can be used to characterize impedance behavior of nanoparticles measuring directly in the colloidal suspension [14]. Colloidal suspensions are habitually analyzed in the range of kHz until MHz where the impedance spectrum is a consequence of the polarization of the nanoparticle double layer, and to the electrodes interfaces polarization. This frequency region is regularly called Alfa Dielectric Dispersion [15] or Low Frequency Dielectric Dispersion.

The standard electro-kinetic models for colloidal suspensions are based on extensive theories [15] [16] [17] [18] [19], and even electro-kinetic phenomenon are still not well understood. The presence of nanoparticles alters electrically the aqueous media due to the formation of doubles layers surrounding the nanoparticles. For instance: experiments of a polystyrene colloidal suspension [20] showed that the suspension permittivity increment decays with the nanoparticles concentration increase. A study about electrical impedance spectra of colloidal silica nanoparticles [21], showed a decrease in conductivity when increasing the size of the nanoparticle. It has also been observed that the silica nanoparticles surface charge density [22] increases with increasing pH, and more recently it has been seen that keeping constant the salt concentration and pH, the surface charge density decreases with an increase in the nanoparticle size until reaching a value independent on the nanoparticle size. Among the variables to be taken into account with the colloidal nanoparticles are: material, shape, size, pH, concentration of the nanoparticles, conductivity and salt concentration of the solution where they are dispersed. Moreover, other physical properties depend on characteristic of the suspension, for instances, studies have showed that the surface tension increases [23] with increasing nanoparticle sizes and nanoparticle bulk densities.

With regard to electrical spectroscopy impedance, R. Roldan et al [24] proposed an empirical Randles circuit model for a sample of 600nm polystyrene colloidal suspension of 1mM KCl diluted in distilled water as solution, measuring with a system of two parallel circular electrodes in the wide frequency range from 20Hz-10GHz. They checked that the electrode-electrolyte interface impedance can be considered as a constant phase element which is added in series to the suspension response without spooling the suspension response. However, R. Roldan et al did not give a physical meaning to each modeled component.

2

To our knowledge, no study has been focused on finding the impedance spectroscopy differences between the silica and polystyrene nanoparticle materials using only water as a solution while the shape, size and nanoparticles concentration remain fixed. In this work, we analyzed and modelled the impedance spectroscopy characteristics of two dispersions: 295-nm silica and 300-nm polystyrene nanoparticles dispersed in deionized water. In order to obtain the impedance dispersion effect of the nanoparticles material in the suspension, we choose monodisperse nanoparticles with a same volume fraction of dispersed solids of 5% and additionally a volume fraction of 2.5% was used. Moreover, we use two specially designed measurement cells with the objective of comparing results between the colloidal suspensions, and we propose two suitable models distinguishing variations due to the geometry of the electrodes of each measurement cell.

2.

Materials and Methods

Monodisperse (295-nm diameter) silica and (300-nm diameter) polystyrene colloidal suspensions were brought to Microparticles GmbH. The volume fraction of dispersed solids was 5 w/v % for both colloidal suspensions. The experiments were carried out using two different measuring systems with two electrodes.

Figure 1. Images of the two different measuring systems with two electrodes: (A) Two parallel aluminum electrodes immersed in the colloidal suspension. (B) Measurement cell made of two parallel stainless steel electrodes clamped in a methacrylate vessel. (C) Measurement cell connected to the impedance analyzer. (D) Colloidal suspension poured in the measurement cell.

3

The first measuring system was two parallel aluminum wires of 1 mm diameter as electrodes. The electrodes were separated 5 mm one to each other and immersed 10 mm in a 50 mL suspension contained in the original factory bottle. Figure.1(A) shows how the electrodes are connected by a four-terminal probe to a Hioki IM3590 impedance analyzer, which was configured with a frequency sweep from 0.1 Hz to 100 kHz with an excitation voltage of 50 mV without bias voltage. Open and short circuit compensation was carried out to correct the effect of cables parasitic impedances. The second measurement system consisted of two parallel square stainless steel plates of 4cm side and separated 3cm one to each other. As it can be seen in Figure.1(B), the measurement cell was a methacrylate vessel fabricated with a CNC-milling machine, the vessel interior dimensions were 4.8 cm x 3.2 cm x 4 cm (large x wide x high). A Hioki IM3590 impedance analyzer was used to measure the suspensions from 0.1 Hz to 200 kHz and an Agilent 4294A impedance analyzer from 200 kHz to 5 MHz (Figure.1(C)). Open and short circuit cable compensation was carried out with both impedance analyzers. As it is observed in Figure.1D, the cell was filled with the 50mL suspension reaching an approximate level of 3.2cm. Then, 25 mL of the suspensions are diluted with 25 mL volume deionized water (4 µS/cm and pH=6) to reach a nanoparticles volume fraction of 2.5 w/v % in order to be also characterize. Before and after each measurement, the cell was rinsed with isopropanol and abundant deionized water and then dried under nitrogen flow in a clean room facility. Additionally, a standard solution with deionized water was also characterized with this measurement cell. Finally, the conductivity and acidity of the suspensions were measured using a Laquatwin EC-33 and Laquatwin-pH-33 respectively.

3.

Results and discussion

3.1. Impedance spectroscopy characterization using two parallel aluminum wire electrodes system

Silica and polystyrene suspensions were measured with the first system and successfully fitted with an expanded Randle model formed by nine distributed elements including the usual configuration: four constant-phase elements (CPE), four leakage resistances (R) and a parallel capacitance (CP), the equivalent circuit is depicted in Figure.2(A). A constant phase element impedance (ZCPE) [25] is defined by equations (1). Where Qi is a no ideal capacitor, α is a dispersion exponent less than or equal to one.

=

1

1

4

Table 1 shows the fitting parameters of the nanoparticles suspensions based on the equivalent circuit from the Figure.2(A), where the first sub-circuit (QE1, αE1, RE1) and fourth sub-circuit (QE2, αE2, RE2) essentially dominate the low frequency region behavior. The second sub-circuit (Qwater, αwater, Rwater) and third sub-circuit (QDL, αDL, RDL) control the behavior at the high and middle frequency region. The estimated relaxation frequency of each sub-circuit can be evaluated using the equation 2:

=

1 2

1

2

Table.1. Fitting parameter for the equivalent circuit of the silica and polystyrene nanoparticles suspensions (s=jω). Colloid

QE1

α1

µFsα-1

RE1

Qwater

MΩ

pFsα-1

αwater

Rwater

QDL

kΩ

µFsα-1

αDL

RDL

QE2

kΩ

µFsα-1

αE2

RE2 MΩ

5% Silica

0.80

0.88

1.4

40

0.94

2.29

2.10

0.82

25.0

2.60

0.90

3.30

5% Polystyrene

1.20

0.92

0.7

60

0.95

0.30

2.10

0.81

25.0

2.60

0.91

0.32

Figure.2. (A) Circuit model used to fit the Nyquist plot of silica and polystyrene nanoparticles colloidal dispersions. We consider the contribution of the Electrodes Polarization by the elements CPEE1, RE1, CPEE2 and RE2. (B) Set-up Diagram of the measurements with a Two-Al-wire as electrodes.

The parallel capacitance CP represents the stray capacitance due to the no immersed aluminum electrodes parts in the liquid. The capacitance of two parallel wires [26] is calculated using the theoretical equation (3):

5

=

3

Where L (7cm) is the length of the wires no immersed, r (0.5 mm) is the wire radius, x (5 mm) is the separation between the wire centers and ε (8.85x10-12 F/m) is the air permittivity. As the CP value is 0.85 pF, a very low capacitance, therefore it can be negligible. The electrode-liquid interfaces impedances are obtained when colloidal suspensions or any aqueous solutions [27] are measured with two electrodes. These impedances observed in series to the nanoparticles suspension impedance are known as Electrode Polarization (EP) effect. The EP effect impedance is capable on certain occasions to be large enough to hide the correct suspension impedance spectroscopy response. As it can be seen in Figure.2, the EP effect is taken into account in the model with the first and fourth sub-circuits, where the relaxation frequency is around of 19 mHz and 250 mHz, respectively. Regarding to the two middle sub-circuits, we consider that they represent the suspension response. The third sub-circuit is associated to a relaxation process into the double layer of the nanoparticles while the second circuit is related to a relaxation process away from the double layer (the H2O). The relaxation frequency for the third sub-circuit is 5.8 Hz for silica and 6.1 Hz for polystyrene, meanwhile the relaxation frequency for the second sub-circuit is 4.89 MHz and 2.26 MHz for silica and polystyrene nanoparticles respectively.

6

Figure.3. Impedance spectroscopy of silica and polystyrene nanoparticles colloidal suspensions showing the good matching of (■) measured with the (▬▬) modeled 295-nm-SiO2 dispersion, and the (▼) measured with (▬▬) the modeled 300-nm-PS dispersion: (A) Nyquist plot, (B) Impedance real part plot, (C) Impedance imaginary part plot, (D) Phase Bode plot. Furthermore, polystyrene nanoparticles exhibit better capacitive behavior from 1Hz to 2.4KHz.

Figure.3 shows the good fitting of the Nyquist and Bode plots for silica (SiO2) and polystyrene nanoparticles (PS) suspensions. The phase plot (Figure.3(D)) was the most hard to fit throughout the entire frequency range. In general, phase plots may be very poorly fitted even though the Nyquist seems well fitted. Synthesizing the results of both nanoparticles suspensions at low frequencies, it seems that silica nanoparticles suspension exhibits better behavior as capacitor than polystyrene suspension since it has a straighter Nyquist line and its phase angle closer to 90 degrees, as it is observed in Figure.3(A) and Figure.3(D). However, the situation changes from 1 Hz to 2.4 kHz where the values of the phase are better for the PS suspension.

After 1 Hz, polystyrene suspension has better capacitive behavior because the impedance real part is lower than silica suspension as it is observed in Figure.3(B), meaning a higher conductivity of the polystyrene suspension. We are not sure why this happens, maybe the transport of ions is less hampered by the hydrophobic nature of the polystyrene surface. Impedance imaginary part showed in Figure.3(C) describes that the nanoparticles suspensions have a similar behavior, likely due to the fact that both suspensions maintain the same size, shape and concentration. The peak observed for polystyrene suspension is due to relaxation of one electrode at 250 mHz.

As the third sub-circuit is due to the nanoparticle double layer, QDL is an indication of the counter-ions charges contained in the double layer and RDL is the surface resistance of the nanoparticles inside the double layer. In contrast, Qwater represents accumulated charges in the water away from the double layer, and Rwater is a resistance of free ions in the water. The fact that RDL>Rwater for both nanoparticle suspensions, in our opinion, may mean that it is easier for a charge to move outside the double layer, where it does not find any obstacle, than when penetrating and leaving the double layer. On the other hand, since the values QDL and RDL are identical for both nanoparticles, we can conclude that the double layer has an identical behavior for both materials. In other words, the double layer in a deionized water medium was virtually independent on the dielectric constant of the nanoparticle when the shape, size and concentration of the nanoparticles are identical. Moreover, due to the nanoparticles relaxation frequency of 5.8 Hz and 6.1 Hz, the double layer tends to polarize to the same speed in the silica nanoparticles as in polystyrene nanoparticles.

7

Y. Zhao et all [28] found experimentally that the nanoparticle relaxation frequency has an inverse relation with the square of the size of the silica nanoparticle. Using the adjustment curve presented by Y. Zhao, the relaxation frequency for 295-nm silica nanoparticles (5 w/v %) can be estimated at 10 kHz. Consequently, our results do not match with the expected values. The displacement of relaxation frequency measured with our samples can be a combination of the following factors: 1.- To the shape of the nanoparticles, ours are spherical and monodisperses [29], while they used slightly opals and milky [30]. 2.- To the pre-treatment of the nanoparticles before measuring. We used those of the nanoparticles manufacturer without making any changes, while they deionized the nanoparticles with a mixed bed ion exchange resin and then diluted it in deionized water. 3.- To the different measurement system and geometry of the electrodes, they used a two electrode probe with a carbon electrode and a stainless steel electrode. Finally, they used an alternating excitation voltage of 1 Volt which we consider it is a bit excessive to keep a pseudo-linear response.

3.2. Impedance spectroscopy characterization using two parallel square stainless steel electrodes. Electrical impedance spectroscopy data for silica and polystyrene suspensions are acquired using the second system (two parallel square stainless steel electrodes) and modelled using the equivalent circuit showed in Figure.4. Some changes are observed with respect to the previous model. The electrode polarization impedance is represented by the first sub-circuit constitutes by CPEE and RE. Since the microscopic irregularities are insignificant in these electrodes that provide a large contact area with the suspension, the electrodes have practically the same polarization, therefore a single sub-circuit can represent the polarizations of both electrodes. Nonetheless, each individual electrode interface should have elements about of 2CPEE and ½ RE.

On the other hand, the sub-circuit due to nanoparticle double layer has disappeared in this circuit. Thus, second subcircuit is the joint response of water and nanoparticles, and Rsusp and Qsusp are the electrical resistance and capacitance of the suspension. Furthermore, the second sub-circuit has a Warburg impedance contribution, which is attributed to ions diffusion due to the larger distance between the stainless steel electrodes than aluminum electrodes and to small nonhomogeneities in the concentration of nanoparticles.

The capacitance CP is a stray capacitance due to air parallel plate capacitor located above the suspension (Figure.1(D)). Since the area of the electrodes without contact with suspension is 4 cm x 0.8 cm, CP is 94 fF. Therefore, this capacitance is negligible.

8

The Table 2 shows the fitting parameters of the nanoparticles suspensions and a deionized water solution, including suspensions with a nanoparticles volume fraction of 5% and 2.5%. Besides, the average and standard deviation values of the conductivity and pH of the solutions measured with a conductivity-meter and a pH-meter are showed in Table 2 so as to use statistically reliable measures.

Figure 4. Equivalent circuit for the impedance spectroscopy modelling using the impedance cell. CPEE, RE are the contribution of the electrodes. CPEsusp, Rsusp, Zwsusp are the contribution of the suspension.

Table 2. Fitting parameter for the equivalent circuit of a standard solution, silica and polystyrene nanoparticles suspensions Solution

QE

α

µFsα-1

RE

Qsusp

kΩ

pFsα-1

αsusp

Rsusp

Asusp

Lcables

Conductivity

kΩ

ΩS1/2

nH

µS/cm

pH

Water solution

210

0.88

38

33

1.0

3.90

900

100

69.5±0.7%

-

5% Silica

399

0.85

28

32

1.0

0.430

25

100

551.5±0.4%

9.9±0.9%

5% Polystyrene

330

0.81

900

38

1.0

0.095

33

100

2567±1.6%

3.0±2.7%

2.5% Silica

380

0.85

36

35

1.0

0.680

25

100

318.6±1%

6.8±8.4%

2.5% Polystyrene

520

0.81

120

38

1.0

0.168

33

100

1241±3.6%

3.5±10.8%

Figure.5(A) shows the Nyquist plot for the solutions modelled in Table 2. The tail of the Nyquist plot is due to first subcircuit and to Warburg element. The first sub-circuit represents the EP impedance because the resonant frequencies for the standard solution, silica suspension (5 w/v %) and polystyrene suspension (5w/v %) are 15 mHz, 9 mHz and 0.14 mHz respectively. The EP impedance also works at low resonant frequencies of 7 mHz and 0.51 mHz when the volume fraction is 2.5%. Another parameter is the Warburg impedance, Table.2 shows that the Warburg coefficient Asusp decreases significantly when the water contains nanoparticles. This means that the nanoparticles provide the charge diffusion. The modeling does not reveal any significant change in Asusp as the volume fraction decreases. The Warburg impedance used in the model is defined by equation (4):

=

√2"

#% $

4 9

The semicircle of the Nyquist plot is associated to Rsusp, so the semicircle decreases as Rsusp decreases and then when the conductivity increases. The water solution without nanoparticles is not very conductive so its semicircle is the largest observed in Figure.5(A). In contrast, the 5% polystyrene nanoparticles suspension has the lowest Rsusp value and the semicircle decreases so much that it disappears. Hence, we elucidate the same conclusion as in section 3.1, polystyrene nanoparticles suspensions are the most conductive solution. In fact, for a volume fraction of 5%, polystyrene nanoparticles suspension is 4.5 more conductive than silica nanoparticle suspension.

Figure.5. Impedance spectroscopy of silica (5% (■), 2.5% (□)) and polystyrene (5% (▼), 2.5% ( )) nanoparticles colloidal suspensions and (●) standard solution with conductivity of 69.5µS/cm: (A) Nyquist plot, (B) Impedance real part plot, (C) Impedance imaginary part plot, (D) Phase Bode plot. Both suspensions exhibit resistive behavior.

For a volume fraction of 2.5%, the polystyrene nanoparticles suspension is also more conductive than silica nanoparticles suspension. The Rsusp rate between silica and polystyrene is 4.1, this little change compared to the volume fraction of 5% means that the addition of deionized water gradually increases the Rsusp in both suspensions. The increment of the Rsusp is reasonable because the added deionized water has a very low conductivity of 4µS/cm decreasing the both suspension conductivities.

10

Figure.5(B) shows the impedance real part bode plot for silica and polystyrene suspensions. The low frequencies region, where the impedance decreases as frequencies increases, is due to the EP impedance (QE and RE). The region of constant impedance is due to the nanoparticles suspension, that is the Rsusp. In this region the silica nanoparticles suspension impedance always has higher impedance values than polystyrene nanoparticles suspension, for example a factor of 4.4 at 1.08kHz for a volume fraction of 5% confirming the good prediction of the model. The pH showed in Table.2 indicates a higher amount of hydrogens (H+) ions in polystyrene suspension than in silica suspension for a common volume fraction of 5%. When the volume fraction is fixed to 2.5%, the concentration of hydrogens almost does not vary in the polystyrene suspension, whereas the silica suspension has become practically neutral (pH=6.8). Therefore, the concentration of free hydrogen or hydroxyl ions does not seem to be related to the higher conductivity of the polystyrene suspension. We believe that the higher conductivity of the PS suspension can be ascribed to hydrophobicity of the PS nanoparticle surface.

In Figure.5(C) is showed the impedance imaginary part of both nanoparticles suspensions. The low frequency region, it is also due to EP impedance, thus 5% polystyrene impedance has higher values than other suspension impedance because its QE has the lowest value of all as it is observed in Table 2. The high frequency region where the impedance increases depends on Rsusp, Qsusp and the inductance of the cables Lcables. Although we did the cables compensation using the measuring instrument, we see that the inductance of the terminal probe is still present. As the volume fraction is decreased to 2.5%, QE value exhibits an increase for the polystyrene suspension. We assume that this is due to a decrease in the amount of nanoparticles adhered to the electrode wall that allows the passage of ions and also improves the electrode electrical contact RE. This increase in charges at the electrode interface could be the explanation for an apparent increase in the dielectric constant when volume fraction decreases that was observed in a previous study [20]. Conversely, QE shows a decrease as the silica nanoparticles volume fraction decreases. According to us, since there are less silica nanoparticles located on the electrode surface, they can no longer attract the same amount of charge and consequently the surface charge density decreases, decreasing the capacitance due to QE. The difference is that the silica nanoparticle has a known silanol group on its surface that make it hydrophilic.

Figure.5(D) shows that the phase curve shifts to the left as the volume fraction decreases, for example a point of -45º moves from 1 Hz to 0.6 Hz for the silica suspension. Moreover, it is observed a resistive behavior of both nanoparticles suspensions because the phase has mostly higher values than -45º. At low frequencies, EP impedance yields phase

11

values lower than -45º likely due to the capacitive behavior of its electrical double layer. Hence, we can conclude that the resistive or capacitive behavior of the nanoparticles suspensions depend on the geometry of the measuring electrodes system.

3.3 Comparison between the two electrodes cell. Table 3 summarizes the conductivity σS of different solutions tested with a conductivity-meter, and also shows the cell constant of the two measurement cells quantified of multiplying the suspension resistance or water resistance by conductivity. Interestingly, for the two parallel square stainless steel electrodes cell, the calculated values are 0.269 cm1

, 0.237 cm-1, 0.246 cm-1, 0.217 cm-1 and 0.208 cm-1 for the standard solution, 5% silica, 5% polystyrene, 2.5% silica

and 2.5% polystyrene suspensions respectively. These values are closed to the theoretical value of the cell constant of 0.234 cm-1 that relates the distance of the electrodes to the area of the cell. This confirms our assumption that the Rsusp is the electrical resistance of the suspension. The different value of the cell constant for polystyrene can be due to some human inaccuracy in the exact volume poured into the cell, to the different meniscuses that form on the walls of the cells that vary the geometry of the suspension with the electrodes and in addition to small bubbles. We believe that a way to improve accuracy would be to always fill the cell completely. On the other hand, using the two aluminum electrodes cell, the values of multiplying Rwater by σS were 0.71 cm-1 and 0.603 cm-1 for silica suspension and polystyrene suspension respectively, thus indicating that there was also some inaccuracy to keep the identical geometry in the two measurements, but we consider acceptable for our purposes. Possibly if the electrodes are more submerged in the suspension, the accuracy would improve. The standard deviation of the suspensions conductivities is in the range of 0.8% to 3.6% with respect to the average value. Although the standard deviations are low, the conductivity-meter also represents a source of error in the calculation of the cell constant.

Table 3. Comparison of different tests carried out with the two impedance measuring cells Type of Cell

Aluminum wire electrodes

Square stainless steel electrodes

Solution

Conductivity σS

Cell constant -1

Max SD of Z’

Max SD of Z’’

µS/cm

cm

%

%

5% Silica suspension

310±0.8%

0.710

7.5

8.1

5% Polystyrene suspension

2010±1.1%

0.603

9.7

11

Standard water solution

69.5±0.7%

0.269

0.3

2.1

5% Silica suspension

551.5±0.4%

0.237

1.2

4.2

5% Polystyrene suspension

2567±1.6%

0.246

3.7

5.1

2.5% Silica suspension

318.6±1%

0.217

1.1

7.7

2.5% Polystyrene suspension

1241±3.6%

0.208

2.1

1.9

12

It should be noticed that the silica suspension conductivity has increased its value from first measurement to the second measurement. This may be because the tests were carried out in different days and due to the fact that colloidal suspension absorbs moisture and residues from the environment [31] [32]. In order to get the standard derivation of impedance parts, we did several consecutive impedance spectroscopy measurements in five minute intervals. Table 3 shows the maximum standard derivation of Z’ and Z’’ obtained for the all samples and measurement systems in the mutual frequency range from 0.1Hz to 100kHz. We find out that the aluminum wire electrodes system has more scattered values. We can conclude that both measurement systems can be used to measure the conductivity of the colloidal nanoparticles and aqueous solutions with low conductivity. Both methods showed that the polystyrene nanoparticles suspension is more conductive than silica nanoparticles suspension. However, square stainless steel electrodes system is more reliable in terms of accuracy.

Another important electrical parameter is the capacitance, which is an indication of the total electrical charge contains both in the suspension and in the interface-electrodes. Therefore, the capacitance as a function of frequency can be evaluated using the equation 5:

=−

2

′′ 5 | |$

The capacitances obtained using both measurement cells can be observed in figure.6. Obviously, the capacitance for the two aluminum wire electrodes is lower than stainless steel electrodes because the electrodes area is lower. We can deduce that the capacitance is mainly contributed by double layers of electrodes-suspension interfaces (QE >> Qsusp) and the nanoparticles-water interfaces (QDL >> Qwater). As frequency increases, QE1, QE2, QDL or QE loss their effects, because the double layers cannot follow the electric field at high frequencies, and the small Qwater or Qsusp begins to contribute with the capacitance. Over a wide frequency range the capacitance of the polystyrene suspensions are higher than silica suspensions because Qsusp-PS > Qsusp-silica. Above 200kHz, the capacitances tend to a very low and nearly same value as it can see in Figure.6(B).

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Figure.6. Capacitance of 295-nm silica (5% (■), 2.5% (□)) and 300-nm polystyrene (5% (▼), 2.5% ( )) nanoparticles colloidal suspensions: (A) measured with the two aluminum wire electrodes in the frequencies range from 0.1Hz to 100kHz. (B) measured with the two square stainless steel electrodes in the frequencies range from 0.1Hz to 5MHz. Furthermore, it is confirmed that polystyrene nanoparticles exhibited a higher electric charge storage than silica nanoparticles over a wife frequency range.

4.

Conclusions

In this work, we have analyzed and modelled the impedance spectroscopy of silica and polystyrene colloidal suspensions in deionized water. Since we maintain the size (295 nm and 300 nm), shape (spherical) and volume fraction of dispersed solids (5 w/v % and 2.5 w/v%), the response obtained is strictly due to the material and its interaction with aqueous medium and the electrodes. The measurements were carried out first with two aluminum wire electrodes system, and then with two square stainless steel electrodes systems. The impedance model for the first two electrodes system consisted of four sub-circuits that allow to detect the electrode polarization at the low frequency region, the nanoparticle double layer and the water responses at the medium and high frequency region. The nanoparticles relaxation frequencies were approximately 6 Hz for both colloidal suspensions with a volume fraction of 5 %. The impedance model for the second two electrode system is formed by two sub-circuit to identify the electrode polarization and suspension response without distinguishing the nanoparticle double layer. Moreover, this model includes a Warburg element, which is attributed to ions diffusion due to some small non-homogeneities in the concentration of nanoparticles between the two electrodes. The Warburg element did not show any significant change when the volume fraction decreased to 2.5 %. Both measurement systems show that the polystyrene nanoparticles suspension has higher conductivity than silica suspension. Using an appropriate calibration from the cell constant, these two electrodes systems can be used to

14

measure the conductivity of colloidal suspensions, but the square stainless steel electrodes system showed to be more reliable in terms of accuracy. The conductivity measured with a separate conductivity-meter is associated in the models to Rsusp or Rwater which increases as the volume fraction decreases. The higher conductivity in the polystyrene suspension is likely due to its hydrophilic surface. The electrode polarization has a very significant effect over the capacitance in a wide frequency range. However, the electrode resistance and capacitance exhibit a contrary behavior with the variation of the volume fraction for the silica and polystyrene colloidal suspensions. As a main conclusion, the differences found in suspensions arise because of the hydrophilic and hydrophobic nature of the silica and polystyrene nanoparticle surfaces.

Acknowledgments This work has been partially supported by the Spanish Ministry of Science and Innovation under projects TEC201782305-R, RTI2018-098728-B-C33, by the European Space Agency under project ESA AO/1-8876/17/NL/CRS and by the SENESCYT of the republic of Ecuador under agreement 2016-AR5G8871. The authors thank Miguel Garcia by the fabrication of the measurement cell.

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Highlights The impedance spectra of 295-nm silica and 300-nm polystyrene nanoparticles dispersed in deionized water at the same concentration, are analyzed and modelled. Two different two-electrode systems have been designed to measure the impedance of silica and polystyrene nanoparticles colloidal suspensions. The electrode polarization response, suspension response and nanoparticle double layer response are interpreted as sub-circuits of an equivalent Randles circuit. Polystyrene nanoparticles suspension exhibits higher conductivity than silica suspension due to the hydrophobic nature of the nanoparticle surface.