Viscosity and Wetting Property of Water Confined in Extended

Aug 15, 2012 - Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan. ABSTRACT: ...
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Viscosity and Wetting Property of Water Confined in Extended Nanospace Simultaneously Measured from Highly-Pressurized Meniscus Motion Lixiao Li,† Yutaka Kazoe,‡ Kazuma Mawatari,†,‡ Yasuhiko Sugii,‡ and Takehiko Kitamori*,†,‡ †

Department of Bioengineering, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan

‡

ABSTRACT: Understanding fluid and interfacial properties in extended nanospace (10− 1000 nm) is important for recent advances of nanofluidics. We studied properties of water confined in fused-silica nanochannels of 50−1500 nm sizes with two types of crosssection: (1) square channel of nanoscale width and depth, and (2) plate channel of microscale width and nanoscale depth. Viscosity and wetting property were simultaneously measured from capillary filling controlled by megapascal external pressure. The viscosity increased in extended nanospace, while the wetting property was almost constant. Especially, water in the square nanochannels had much higher viscosity than the plate channel, which can be explained considering loosely coupled water molecules by hydrogen bond on the surface within 24 nm. This study suggests specificity of fluids twodimensionally confined in extended nanoscale, in which the liquid is highly viscous by the specific water phase, while the wetting dynamics is governed by the well-known adsorbed water layer of several-molecules thickness. SECTION: Liquids; Chemical and Dynamical Processes in Solution

A

through water molecules. This hypothesis for confined liquid has been further supported by other studies showing lower permittivity and higher proton diffusion coefficient.13,14 Moreover, effects of an ion screening layer to cancel an electric charge of the surface, i.e., electric double layer, become dominant in extended nanospace because of comparable thickness to the size determined by the Debye length.15 Many researchers have studied electroviscous effect where the fluid is affected by electric body force induced by ion drag of the electric double layer.16 These results for confined liquids suggest that, even for extended nanospace, the fluidic and interfacial properties of liquids can be significantly affected by the surface interactions. In addition to the space size, the dimension of the confinement is also expected to be important, since it changes potential energies for electrostatic interactions and molecular behaviors. Therefore, study of fluidic and interfacial properties in extended nanospace, for various channel sizes and channel shapes with different confinement dimensions, is required to establish nanofluid dynamics fundamentals to develop novel devices for various applications using specific properties of nanospaces. Experimental investigation of fluid behavior confined in nanochannels has been difficult owing to the small space size. Measuring capillary filling speed is one approach to reveal fluidic and interfacial properties in small channels because of its

s micro/nanotechnologies have been rapidly developed, research and engineering fields in biology, analytical chemistry, and semiconductor industry are shifting from microspace to nanospace. Nanofluidics is fundamental for engineering in order to realize manipulation and sensing of molecules with a comparable dimension to the space size.1−3 Liquid behaviors in nanospace have therefore become more important in the past decades. Traditionally, many researchers in colloid and geophysical science have revealed strong interfacial forces across a thin liquid film between two plates of nanometer-order distance, which are strongly related to the structure of water on the surface.4−8 For confined 0.1−10 nm space such as nanopore and carbon nanotubes, recent studies have reported a number of unique properties including liquid structure and phase transition due to oriented behavior of molecules.9,10 On the other hand, 10−1000 nm space, which we call extended nanospace, is more suitable for fluidic systems, including recent chemical analysis devices and inter/intracellular spaces, with collective behavior of liquid molecules in a transitional regime from single molecules to condensed phase. Our recent NMR studies have revealed that the proton exchange rate in water increases with decreasing sizes of fusedsilica extended nanochannels.11,12 These results suggested the presence of a proton transfer phase of loosely coupled water molecules by hydrogen bonding in the vicinity of the wall within 50 nm, which is much thicker than the well-known adsorbed water layer of several-molecules thickness on hydrophilic surfaces.5,6,8 It is considered that this specific liquid structure in extended nanospace enhances proton hopping © 2012 American Chemical Society

Received: July 11, 2012 Accepted: August 15, 2012 Published: August 15, 2012 2447

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Figure 1. (a) Schematic of experimental setup for observation of capillary filling into the fused-silica nanochannels driven by the high-pressure control system using compressed air. (b) Cross-sectional views of square and plate nanochannels.

comparable to the Laplace pressure. A pressure-driven flow control technique established by our group was used for the method.26,27 Results show the specific property of the square nanochannels where liquid molecules are two-dimensionally confined in nanoscale, compared with the plate nanochannels with nanoconfinement only in the depthwise direction. The results are further discussed considering a boundary water layer of specific liquid structure. Figure 1 illustrates a schematic of an experimental apparatus. Various nanochannels of different sizes were prepared as listed in Table 1 with two types of cross-sectional shape: square

principle described by Washburn.17 Churayev and co-workers have studied capillary filing for fluid viscosity and wetting dynamics in quartz nanocapillaries.18,19 The results suggested that water viscosity increases for capillaries of diameters smaller than 1000 nm, 1.4 times higher viscosity in an 84 nm capillary than the bulk, and dynamic contact angle depends on the meniscus motion. However, there is uncertainty of capillary size because the radius was indirectly predicted from the injection pressure. Recently, we have developed accurate nanofabrication methods and measured the filling speed of water in a fusedsilica nanochannel with a 330 nm hydrodynamic diameter, showing higher viscosity.13 On the other hand, studies of capillary filling in plate nanochannels (microscale width and nanoscale depth) suggested that the specificity of nanoscale aqueous liquids is observed in channels smaller than 100 nm.20−22 Haneveld et al. showed that the viscosity increases to 1.3 times at 11 nm depth, which indicates much smaller confinement effect than our results.21 Several factors for the specificity in nanochannels have been suggested, including structured water near the boundary,13,21 electroviscous effect20,23 and bubble formation during filling process.24,25 However, the cause of the phenomena is still unknown because the previous results are not consistent, showing different size dependency and different values. Especially, there is no report showing consistent results for different channel shapes of different confinement dimension. In order to reveal liquid properties in nanochannels by the capillary filling, the wetting property of liquid in nanochannels must be evaluated because the capillary filling is dependent on both fluidic and interfacial properties. However, most of the previous studies have taken the effect of wetting dynamics into account by evaluating contact angle in the bulk scale. Therefore, a simultaneous measurement method for fluidic and interfacial properties in nanochannel is required, in addition to accurate nanofabrication and flow control methods. In this study, we investigated the water properties in accurately fabricated 50−1500 nm fused silica extended nanochannels of two types of cross sections: (1) square channel of nanoscale width and depth, and (2) plate channel of microscale width and nanoscale depth. A method to simultaneously obtain the fluid viscosity and wetting property was developed by controlling the meniscus motion in the nanochannel applying megapascal order external pressure

Table 1. Sizes of Square and Plate Nanochannelsa channel type square channel, W ≈ D

plate channel, W/D > 20

representative size (nm)

width, W (nm)

depth, D (nm)

200 ± 8 393 ± 16 491 ± 13 838 ± 16 1112 ± 24 1530 ± 26 25 ± 1 50 ± 1 100 ± 1 189 ± 4 415 ± 6

212 ± 17 374 ± 29 519 ± 26 712 ± 23 1183 ± 53 1559 ± 53 20000 20000 20000 20000 20000

189 ± 4 415 ± 6 466 ± 11 1017 ± 3 1049 ± 13 1503 ± 11b 25 ± 1 50 ± 1 100 ± 1 189 ± 4 415 ± 6

a The channel length is 300 μm for the square channel and 2 mm for the plate channel. bSince AFM could not be applied for 1500 nm, the depth was estimated from an etching rate of 1.14 nm/s.

nanochannel with an aspect ratio of 1 (D = W) for twodimensional nanoconfinement of liquid, and plate nanochannel with an aspect ratio larger than 20 (W/D > 20) for onedimensional nanoconfinement, where D is the channel depth and W is the width. Even for the smallest sizes, nanochannels were accurately fabricated as shown in Figure 2. The representative size of nanochannel is the hydrodynamic diameter Dh = 2DW/(D + W) for the square channels and the channel depth D for the plate channels. A method to simultaneously evaluate fluidic and interfacial properties of liquid in extended nanochannel was developed using the capillary filling speed. Generally, capillary filling occurs spontaneously depending on both the fluidic resistance 2448

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surface tension, and dynamic contract angle are constant. Therefore, the liquid viscosity μ and the surface tension force showing the wetting property, defined as a force parallel to the channel derived from the surface tension, γ cos θ, can be obtained from a slope and intercept of a fitting line of the relationship between Δx2/Δt and Pex. Measurements were conducted for the pressure-driven capillary filling of water into the nanochannel. Since the Laplace pressure in nanoscale is megapascal order, the external pressure applied to the nanochannel must also be megapascal to control the meniscus motion. Hence, a high-pressure control system with a maximum pressure of 4.5 MPa, which was recently developed by our group,27 was used. The external pressure applied to the nanochannel Pex was regarded as the value generated by the pressure control system because of the dominant pressure drop in the nanochannel (as mentioned in the Experimental Methods). The meniscus motion as liquid filled into the nanochannel was recorded by an inverted brightfield microscope equipped with a high-speed camera as shown in Figure 3. In order to satisfy the negligible pressure drop of gas phase in eq 1, ΔPliq ≫ ΔPgas, the meniscus positions of x ≫

Figure 2. Size of nanochannels evaluated by SEM and AFM for (a) 200 nm square nanochannel and (b) 25 nm plate nanochannel [(1) SEM image for evaluation of the channel width; (2) channel profile obtained by AFM for evaluation of channel depth]. Noted that the channel depth measured by AFM is obtained from a reference channel of microscale width fabricated on the same fused-silica substrate as the nanochannel, since it is difficult to apply AFM to nanoscale width channels.

ΔP and the Laplace pressure PL. In this case, fluid and interfacial properties cannot be obtained separately by measuring the spontaneous filling speed. Therefore, in the present study, an external pressure Pex is applied to the liquid in the nanochannel as shown in Figure 1. The pressure balance of the capillary filling in the steady state is expressed as follows: ΔPliq + ΔPgas = PL + Pex

(1)

where ΔPliq and ΔPgas is the fluidic resistance along the channel for liquid and gas phases, respectively. The fluidic resistance of the gas phase becomes negligible, ΔPliq ≫ ΔPgas, when the length of liquid phase in the nanochannel x is sufficient at x ≫ (L − x)μgas/μ, where L is the nanochannel length, μgas is the gas viscosity, and μ is the liquid viscosity. From the Hagen− Poiseuille law and the Young−Laplace equation, eq 1 for ΔPliq ≫ ΔPgas is integrated for square and plate channels respectively as follows: Square channel:

Plate channel:

4.5D h 2 4.5γD h Δx 2 = Pex + cos θ Δt 64μ 16μ

Dγ cos θ Δx 2 D2 = Pex + Δt 6μ 3μ

(2)

(3)

where Δx = x(t) − x0(t0) is the meniscus displacement from a reference position x0 and Δt = t − t0 is the time difference, γ is the surface tension, and θ is the dynamic contact angle. A coefficient of 4.5 in eq 2 considers a flow profile in the square cross-sectional channel obtained from an analytical solution of the Navier−Stokes equation.28 This modification for the Washburn equation was validated in a previous study of capillary filling into microchannels.29 Equations 2 and 3 show that a ratio between the square of meniscus displacement and the time difference, Δx2/Δt, linearly varies with the external pressure Pex, assuming that the channel size, liquid viscosity,

Figure 3. Instantaneous images of capillary filling for (a) 374 nm square channel and (b) 100 nm plate channel, and relationships between Δx2/Δt and Pex. 2449

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viscosity comparable to a reference of 0.868 × 10−3 Pa s at room temperature of 26.1 °C.32 For the plate nanochannels at sizes smaller than 200 nm, the viscosity increases, and the value at 25 nm becomes 1.2 times higher than 0.826 ± 0.036 × 10−3 Pa s at 415 nm. This tendency is similar to previous results reported by Haneveld et al.21 for thin plate nanochannels. On the other hand, for square nanochannels, the viscosity starts to increase at 900 nm, and that at 200 nm is 2.5 times higher than 0.841 ± 0.032 × 10−3 Pa s at 1559 nm. Compared to the plate nanochannel, the viscosity in the square channel shows unique tendency with much higher values. Several researchers have interpreted the higher viscosity in nanochnanels to be because of electroviscous effect caused by the electric double layer.20,23 However, previous studies using numerical simulation have suggested that the electroviscous effect does not have monotone increase with decreasing size, and the influence is much weaker, comparing with the experimental results.23,25 Therefore, our results suggest there is another factor to enhance the water viscosity, which is dependent on the confinement dimension of liquid in extended nanospaces. The results of the water viscosity in nanochannels were further discussed considering the liquid structure in nanochannels. Previous studies have suggested that there are adsorbed water molecules on a silicon hydroxide surface, which has an ice-like liquid structure of several layers of water molecules.5,6,8 On the other hand, our recent results from NMR measurement for water in square extended nanochannels suggest loosely coupled water molecules by hydrogen bond within 50 nm of the glass wall which enhance the proton mobility, i.e., proton transfer phase.11,12 These studies indicate that there can be a boundary water layer with specific liquid structure on the nanochannel wall. Therefore the present results were analyzed considering the specific water layer with a thickness of λ and viscosity of μλ. Assuming that the measured viscosity is a spatially averaged value in the nanochannel, the measured viscosity is given by the following:

Lμgas/(μ + μgas) were used for the analysis (x ≫ 6 μm for the square channel, x ≫ 39 μm for the plate channel). In addition, Thamdrup et al. has reported that bubble formation in a nanochannel with capillary filling can significantly affect the results.24 Hence nanochannels with bubbles were excluded from the analysis. The results showed that the square of the meniscus displacement Δx2 has a linear relationship with the time Δt as already shown in previous studies,20,24 and Δx2/Δt was obtained from the linear regression with the correlation coefficients of R2 = 0.999 ± 0.001 for all conditions. Figure 3 shows relationships between the ratio of the square of meniscus displacement to the time Δx2/Δt and the external pressure Pex for (a) square and (b) plate nanochannels. Δx2/Δt has a linear relationship with Pex, and the correlation coefficients for the regression were R2 = 0.996 ± 0.004. Although it is well known that the dynamic contact angle has a relationship with the meniscus velocity,30,31 this linear relationship indicates that the dynamic contact angle is almost constant during capillary filling with meniscus velocities controlled by the external pressure. From the slope and intercept of the fitting line, the water viscosity and the surface tension force were simultaneously obtained, as shown in Figure 4. Figure 4a shows measured viscosities of water as a function of the representative channel size. With decreasing channel size, the viscosity increases from the values considered to be the bulk

⎛ λ ⎞2 Square channel: μ = − 4(μλ − μ0 )⎜ ⎟ ⎝ Dh ⎠ λ + 4(μλ − μ0 ) + μ0 Dh Plate channel: μ = −2(μλ − μ0 )

(4)

λ + μ0 Dh

(5) −3

where μ0 is the bulk viscosity of 0.868 × 10 Pa s at room temperature. The fitting lines by eqs 4 and 5 toward the experimental results are shown in Figure 4 (dashed line). From the fitting of the results of the square channels by eq 4 using the data of 200 nm, 393 nm, 491 and 838 nm, the properties of water layer was estimated to be λ = 24 nm and μλ = 3.95 × 10−3 Pa s. This thickness is of similar order to the proton transfer phase of loosely coupled water molecules proposed by our group. On the other hand, for the plate channels by fitting with eq 5 using the data and μλ = 3.95 × 10−3 Pa s, λ = 0.4 nm is in agreement with the thickness of adsorbed water layer on the glass surface, as also reported by Haneveld et al.21 Since the adsorbed water layer exists on the glass surface in the open space, one possible explanation is that only the water confined in the square nanochannels has the specific water phase of 24 nm thickness of similar order to the proton transfer phase. Therefore, we propose the specificity of liquid two-dimension-

Figure 4. (a) Viscosity and (b) surface tension force of water as function of sizes of extended nanochannels. Error bars were estimated from the standard deviation of channel size and coefficients obtained from the linear fitting. Solid line shows the bulk viscosity of 0.868 × 10−3 Pa s at the room temperature of 26.1 °C. Dashed lines show the fitting by eqs 4 and 5 toward the experimental results. 2450

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EXPERIMENTAL METHODS Microchip Fabrication. The nanochannels were fabricated on a fused-silica substrate by electron beam lithography and plasma etching as reported in previous work.20 The channel sizes were evaluated by scanning electron microscope (SEM) for the width and atomic force microscope (AFM) for the depth. Since the depth of square nanochannel cannot be directly measured by AFM owing to the nanoscale width, the channel depth was measured in a reference channel located at a 5 mm distance from the nanochannel. In our previous work, cross-section of the nanochannel was directly observed by scanning electron microscopy, showing successful etching results.12 Therefore it is considered that the square nanochannel was uniformly etched on the fused-silica surface with a depth similar to that of the reference channel. Two U-shaped microchannels (500 μm width, 6 μm depth and 30 mm length from inlet to the connecting point with the nanochannels) were etched on another fused-silica substrate for liquid injection. Afterward, the two glass substrates were thermally bonded at 1080 °C. Nanochannels and microchannels were designed to minimize the hydrodynamic effects of the microchannel on the nanochannel to less than 1%. For example, for the square nanochannel with 200 nm hydrodynamic diameter, 99.98101% of the total pressure drop within all of the channels in the fused-silica microchip is consumed in the nanochannels. Prior to the measurement, the channels were sequentially rinsed by acetone, ethanol, water, NaOH, and water to make the surface clean and hydrophilic. Experimental Procedure. The water used here was treated with a water purification system and had an electrical resistance >18.0 MΩ cm. The liquid temperature was assumed to be at room temperature of 26.1 ± 0.6 °C. The meniscus motion as water filled into the nanochannel was recorded by an inverted bright-field microscope equipped with a high speed camera with a frame rate of 1 kHz for the external pressures of 0−2 MPa. The meniscus position was determined from the obtained images with an error of ±2 pixel, which is negligibly small compared with the meniscus displacement larger than at least 110 pixel during 4 ms in a minimum case.

ally confined in extended nanoscale, which induces the proton transfer phase by dominant surface effects and significantly enhances the viscosity. Figure 4b shows the surface tension force γ cos θ as a function of the channel size. Obvious dependency of the wetting property on the channel size and confinement dimension is not observed, in contrast to the viscosity. Previous studies reported mainly two factors that affect the surface tension force, effects of the meniscus velocity, and the liquid pH on the dynamic contact angle.30,31,33 In this study, average meniscus velocities varied from 1 mm/s at minimum for the 25 nm plate nanochannel to 50 mm/s at maximum for the 1503 nm square channel. For the pH effect, a recent study by our group reported that the pH of water in a fused silica extended nanochannel is lower than that in the bulk (average pH 5 at 400 nm while the bulk pH is 6).34 However, considering the data and error bars, these factors do not significantly affect the results for the water/fused-silica system in extended nanospaces. On the other hand, from a theoretical viewpoint, it is well known that dynamic wetting is described by two models: hydrodynamic model strongly related to the fluid property, and molecular kinetic theory determined by interactions between several layers of liquid molecules and the surface.30 Since the significant difference of viscosity between square and plate nanochannels as shown in Figure 4a is not reflected in the surface tension force, the wetting dynamics in extended nanospace is considered to be governed by molecular kinetic theory. In conclusion, the results suggest that the wetting property is dependent on spaces much smaller than extended nanospace, as proposed by molecular-kinetic theory considering interactions between the surface and several-layered liquid molecules, which have similar scale to the adsorbed water layer. In summary, we investigated the viscosity and wetting property of water in fused-silica extended nanochannels of various sizes with two types of cross-sectional shape: square nanochannel (nanoscale width and depth) and plate nanochannel (microscale width and nanoscale depth). A simultaneous measurement method was developed by controlling the meniscus motion by the external pressure. The results suggest that the water viscosity increases with decreasing the sizes. Especially, water in the square nanochannels was highly viscous compared with that in the plate nanochannels. The result of data fitting suggested that the specific water layer of 24 nm thickness is generated only in the square channel, which has size dependency similar to that of the proton transfer phase of loosely coupled water molecules proposed by our group. On the other hand, the wetting property was almost independent of the channel. This suggested that the wetting dynamics is governed by spaces much smaller than extended nanospace, with similar scales to several layers of liquid molecules corresponding to adsorbed water molecules on the surface. This study proposes specificity of liquid two-dimensionally confined in extended nanoscale, in which the viscosity is highly enhanced by the specific water phase of 24 nm thickness, while wetting dynamics is governed by the adsorbed water layer of several-molecule thickness. This study will contribute to understanding liquid behavior and interface formation in extended nanospace, which is important to establish nanofluidics for novel devices in semiconductor industry and analytical chemistry.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +81−3−5841−7231. Fax: +81−3−5841−6039. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a Grant-in-Aid for Specially Promoted Research from the Japan Society for the Promotion of Science (JSPS) and a JSPS Core-to-Core Program.

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