Dielectric Constant of Liquids Confined in the Extended Nanospace

Letter pubs.acs.org/ac

Dielectric Constant of Liquids Confined in the Extended Nanospace Measured by a Streaming Potential Method Kyojiro Morikawa,† Yutaka Kazoe,‡ Kazuma Mawatari,‡ Takehiko Tsukahara,† and Takehiko Kitamori*,‡ †

Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, 2-12-1-N1-6, O-Okayama, Meguro, Tokyo 152-8550, Japan ‡ Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo 113-8656, Japan ABSTRACT: Understanding liquid structure and the electrical properties of liquids confined in extended nanospaces (10−1000 nm) is important for nanofluidics and nanochemistry. To understand these liquid properties requires determination of the dielectric constant of liquids confined in extended nanospaces. A novel dielectric constant measurement method has thus been developed for extended nanospaces using a streaming potential method. We focused on the nonsteady-state streaming potential in extended nanospaces and successfully measured the dielectric constant of liquids within them without the use of probe molecules. The dielectric constant of water was determined to be significantly reduced by about 3 times compared to that of the bulk. This result contributes key information toward further understanding of the chemistry and fluidics in extended nanospaces.

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while the bulk phase forms a typical liquid water structure. As an intermediate phase between the adsorbed and bulk phases, the proton transfer phase has a highly ordered structure that consists of loosely coupled water molecules within approximately 50 nm from the surface.20,21 These results indicate that water molecules in an extended nanospace are highly oriented, which implies that the dielectric constant may be different from that in the bulk. This has a significant effect on ion behavior and the electrical double layer (EDL) formed by the electrostatic interactions between the surface charge and distributed ions. At present, many unique ion transport phenomena in extended nanospaces have been reported, such as ion separation, ion condensation, and ion rectification.22−27 We have also recently suggested that the distribution of hydrogen ions in a 400 nm extended nanospace, which was measured using stimulated emission depletion (STED) microscopy, can be well explained by numerical simulation using EDL theory with a dielectric constant about 5 times lower than that for the bulk.28 Therefore, dielectric constant measurements of liquids in extended nanospaces are strongly required. There have been many previous efforts to measure the dielectric constants of liquids confined in extended nanospaces. In our previous report, a lower dielectric constant of an aqueous solution in a 330 nm space than that in the bulk was suggested from fluorescence lifetime measurements.29 However, the fluorescent probe molecules may have an effect on the water properties. Other groups performed the electrical

ntegrated chemical systems in microfluidic/nanofluidic research have provided superior performance than that for bulk chemical systems. In the past decade, research and engineering field are shifting from microspace to nanospace. Since nanospace is comparable in the size to individual molecules, liquid behavior in the space is important. In traditional surface force measurements, it has been revealed that water molecules in the region within nanometer order from the surface had ordered structure.1−4 In addition, recent studies reported that water confined in 1−10 nm spaces showed ordered and ice-like structure formation.5−8 Considering the ordered water molecules, a lower dielectric constant of water in nanospaces than that in the bulk was suggested.9−12 On the other hand, 10−1000 nm space is referred to as an extended nanospace to distinguish it from a nanospace in the 1−10 nm range. Unique liquid properties can be expected in an extended nanospace because it represents a transitional regime from single molecules to the bulk condensed phase.13−17 Therefore, it is necessary to have experimental tools to investigate the properties of liquids in extended nanospaces. Recently, our group has developed various experimental tools and revealed many unique liquid properties in an extended nanospace. For example, the fabrication of a size-regulated nanofluidic channel with a minimum dimension of 40 nm was achieved for attoliter to femtoliter (10−18−10−15 L) volume fluidic control with flow rates from picoliters to femtoliters per minute.18,19 In our nuclear magnetic resonance (NMR) studies, water confined in an extended nanospace on a fused silica substrate exhibited slower intermolecular motion and higher proton mobility than those for bulk water. On the basis of these results, we proposed a three-phase model that consists of an adsorbed phase, a proton transfer phase, and a bulk phase. In this model, the adsorbed phase forms an ice-like structure, © 2015 American Chemical Society

Received: November 6, 2014 Accepted: January 8, 2015 Published: January 8, 2015 1475

DOI: 10.1021/ac504141j Anal. Chem. 2015, 87, 1475−1479

Letter

Analytical Chemistry

streaming potential/current generated between Ag-AgCl electrodes was detected using an electrometer. This system is based on the design of fluidic and electrical resistances, so that the potential/current generated by liquid flow in the extended nanospace can be measured, while noise generated in the microspace and bulk can be ignored. All measurements were performed at a room temperature of 20 ± 1 °C. Figure 1 shows schematic illustrations of liquid flow in an extended nanochannel and the electrical equivalent circuit. In

impedance measurement of liquids in nanopores using an alternate current (ac) method.30,31 In these experiments, a voltage was applied to the nanopores using bulk electrodes. However, using this arrangement, signals were obtained from liquids in the nanopores and in the bulk and from the nanopore and electrode materials. Because of the complexity of the electrical circuit, the dielectric constant could not be obtained. Because of the similar problem, our previous work on impedance measurements of liquids in extended nanochannels by the ac method were not successful to obtain dielectric constants in extended nanospaces.32 To overcome such difficulties in the measurements, we have developed a streaming potential/current measurement system for extended nanospaces.33,34 A fluidic system was designed for optimal fluidic and electrical resistances to make the noise generated in the microspace and bulk negligible. Measurements of picoampere (pA) order current generated by proton flow in water confined in an extended nanospace have been realized with this system. This system enables the investigation of water properties without the need for probe molecules. Thus, measurement of the dielectric constant of water confined in an extended nanospace without the use of probe molecules is also expected to be achievable with this system. In the present study, a method to measure the dielectric constant of liquids in an extended nanospace was developed by application of a streaming potential/current measurement system. Focus was made on the nonsteady-state streaming potential, and the capacitances of liquids in an extended nanospace were obtained from the time constants. To relate the capacitance and the dielectric constant, calibration experiments were conducted by changing the sample solvent to determine the cell constant. The dielectric constant of confined water was thus obtained using the cell constant. This is the first demonstration where the dielectric constant of liquids in an extended nanospace has been determined.

Figure 1. Schematic illustration of the streaming potential/current system in an extended nanospace and the equivalent circuit.

the circuit, the streaming current is considered to be the current supplier generated by pressure-driven flow. Because of the design of optimal fluidic and electrical resistances, only the electrical components of the extended nanochannel need be considered. The nonsteady-state streaming potential and time constant were the primary focus. The potential between the extended nanochannel V(t) was gradually increased with time. The process is analogous to charging a battery and is dependent on the channel capacitance, C, and resistance, R. When the current through the capacitor is i(t), the current equation is expressed as

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MATERIALS AND METHODS The procedure for the fabrication of extended nanochannels has been previously reported elsewhere.21 Extended nanochannels were fabricated on a synthetic fused silica plate by electron beam lithography and plasma etching. The width and depth were determined using scanning electron microscopy (SEM) and atomic force microscopy (AFM). From the obtained channel width and depth, the channel size was determined as an equivalent diameter as shown in Table 1. On Table 1. Sizes of Extended Nanochannels

a

V (t ) (1) R Considering that i(t) is the time derivative of the charge in the capacitor, eq 2 is obtained: IS = i(t ) +

i(t ) = C

a

representing size [nm]

width [nm]

depth [nm]

400 800 1460 2020 2500

450 920 1380 2240 2500

360 700 1550 1840 2500

d V (t ) dt

(2)

Using eqs 1 and 2, V(t) is obtained as eq 3 with the boundary condition V (0) = 0: ⎡ ⎛ t ⎞⎤ ⎟ V (t ) = RIS⎢1 − exp⎜ − ⎝ CR ⎠⎥⎦ ⎣

(3)

The nonsteady-state streaming potential is expressed by eq 3. In addition, as t → ∞, the steady-state streaming potential VS, is obtained using eq 4, which satisfies Ohm’s law.

The channel length was 400 μm for all extended nanochannels.

another substrate, microchannels were fabricated for liquid exchange and connected with the extended nanochannels. The two substrates were bonded at 1080 °C by the thermal fusion bonding method. Details of streaming potential/current measurement system have been previously reported.33,34 Sample liquids were introduced into the microchannel and extended nanochannels with a pressure controller, and the

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VS = RIS

(4)

RESULTS AND DISCUSSION The voltage was gradually increased with the application of pressure, and a constant value was reached. Figure 2 shows the voltage change with time, which is in good agreement with eq 1476

DOI: 10.1021/ac504141j Anal. Chem. 2015, 87, 1475−1479

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Analytical Chemistry

Figure 4. Relationship between the dielectric constant and capacitance in a 1480 nm space. The cell constants, (9.0 ± 2.2) × 10−12 in a 1480 nm space and (9.4 ± 1.8) × 10−12 in a 2020 nm space, were obtained from the slope.

Figure 2. Voltage change as a function of time and the fitting result; the channel size was 800 nm and the sample was deionized (DI) water.

3, and the time constant CR, is obtained. The steady-state streaming potential VS and streaming current IS were then measured by changing the applied pressure. The resistance R, was evaluated from the obtained VS and IS. Figure 3 shows VS as a function of IS, which is linear in agreement with eq 4, and R was obtained from the slope. The capacitance C was obtained from the results given in Figures 2 and 3.

Figure 5. Size dependency of the dielectric constant; the sample was DI water.

Figure 3. Relationship between the nonsteady-state streaming potential and the streaming current; the channel size was 800 nm and the sample was DI water.

The cell constant of the setup was next evaluated to calibrate the capacitance values. The relationship between the capacitance value and dielectric constant was evaluated by measurements of various solvents. The samples and their dielectric constants are following; 80 for water, 33 for methanol, 24 for ethanol, and 18 for 2-propanol. The calibration experiments were performed in 1480 and 2020 nm spaces, because the unique liquid properties are not observed in a microspace.21 Results are shown in Figure 4. The average of the measurement values and the standard deviation in 5 times experiments are shown as plots and error bars. Noted that this plot style is also applied to Figures 5 and 6. The capacitance was a linear function of the dielectric constant εr, and the cell constant was obtained from the slope. In addition, the cell constant for the 1480 nm space was the same as that for the 2020 nm space within the measurement error. Thus, the cell constant was independent of the space dimensions and could be applied to all capacitance values that were obtained in the 400−2500 nm spaces.

Figure 6. Relationship between the dielectric constant and the Debye length; the sample was a KCl aqueous solution.

Finally, the dielectric constant of water was obtained from the cell constant, and its size dependence is shown in Figure 5. In a microspace, the same dielectric constant as that for the bulk (εr = 80) was obtained. This indicates that water in a microspace can be treated the same as water in the bulk. However, in the extended nanospaces, the dielectric constant was significantly reduced by about 3 times compared to that for the bulk. One possible reason for the lower dielectric constant is the effect of the EDL, which consists of the Stern layer and diffuse layer. It has been previously reported10 that the Stern layer has a much lower dielectric constant due to the orientation of water 1477

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molecules induced by the high electric field of the surface charge. In this immobile layer, the dielectric constant is assumed to be around 6 in the region 0.3 nm from the surface. However, the 0.3 nm scale is too small to give rise to the threetimes lower dielectric constant in a 400 nm space. On the other hand, in the diffuse layer, the water molecules are significantly polarized under the local electric field and thus have a lower dielectric constant. In bulk scale measurements using AFM,35 lower dielectric constants of aqueous solutions in the region approximately 10 nm from the surface were reported. To evaluate the effect of a diffuse layer on the lower dielectric constant, the relationship between the diffuse layer thickness (Debye length) and the dielectric constant in a 400 nm space was evaluated. The Debye length was changed by changing the concentration of a KCl aqueous solution. Figure 6 shows that the dielectric constant in a 400 nm space had no significant difference in different Debye length. The results also showed that the EDL overlap was not the cause of the lower dielectric constant in an extended nanospace. Therefore, there is no definite correlation between the lower dielectric constant in an extended nanospace and the Debye length. On the other hand, in our recent studies,20,21,36,37 unique liquid properties were observed in 40−800 nm spaces, and we suggested that the proton transfer phase has a highly ordered structure that consists of loosely coupled water molecules within approximately 50 nm from the surface. The size scale of the proton transfer phase was consistent with the size region of the lower dielectric constant obtained in this study. Therefore, the results of this study support the model of a proton transfer phase with highly oriented water molecules within 50 nm of the glass surface. Furthermore, the lower dielectric constant of εr = 17, obtained in our previous experiment and calculation,28 is in approximate agreement with the results obtained in this study. Therefore, this study has been very important with respect to verification of our previous results for a liquid model confined in an extended nanospace.

ACKNOWLEDGMENTS This work was supported by a Grant-in-Aid for Specially Promoted Research and a Grant-in-Aid for JSPS Fellows from the Japan Society for the Promotion of Science (JSPS). We thank Prof. Rossen Sedev and Dr. Craig Priest for the fruitful discussions.

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CONCLUSION A streaming potential/current measurement system was applied to dielectric constant measurements of liquids in extended nanospaces. Focus was made on the nonsteady-state streaming potential, and the capacitances of liquids in extended nanospaces were obtained from the time constants. The dielectric constants were obtained from the cell constant that was determined in the calibration experiments. The dielectric constant of water confined in an extended nanospace was significantly reduced to a value approximately 3 times lower than that for the bulk. This is the first demonstration to determine the dielectric constant in extended nanospaces, and the results support our previous results and models based on heterogeneous liquid structures. Although further experimental and theoretical studies are required to clarify the equivalent circuit model with a heterogeneous liquid structure and an EDL, we believe that the proposed method and the results obtained are valuable contributions to the fields of nanofluidics and nanochemistry.

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Letter

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +81-3-5841-6039. Notes

The authors declare no competing financial interest. 1478

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Analytical Chemistry (34) Morikawa, K.; Mawatari, K.; Kazoe, Y.; Tsukahara, T.; Kitamori, T. Appl. Phys. Lett. 2011, 99, 123115. (35) Teschke, O.; Ceotto, G.; de Souza, E. Chem. Phys. Lett. 2000, 326, 328−334. (36) Li, L.; Kazoe, Y.; Mawatari, K.; Sugii, Y.; Kitamori, T. J. Phys. Chem. Lett. 2012, 3, 2447−2452. (37) Chinen, H.; Mawatari, K.; Pihosh, Y.; Morikawa, K.; Kazoe, Y.; Tsukahara, T.; Kitamori, T. Angew. Chem., Int. Ed. 2012, 51, 3573− 3577.

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