Article pubs.acs.org/Langmuir
Accelerated Sedimentation Velocity Assessment for Nanowires Stabilized in a Non-Newtonian Fluid Chia-Wei Chang and Ying-Chih Liao* Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617 S Supporting Information *
ABSTRACT: In this work, the long-term stability of titanium oxide nanowire suspensions was accessed by an accelerated sedimentation with centrifugal forces. Titanium oxide (TiO2) nanoparticle (NP) and nanowire (NW) dispersions were prepared, and their sizes were carefully characterized. To replace the time-consuming visual observation, sedimentation velocities of the TiO2 NP and NW suspensions were measured using an analytical centrifuge. For an aqueous TiO2 NP suspension, the measured sedimentation velocities were linearly dependent on the relative centrifugal forces (RCF), as predicted by the classical Stokes law. A similar linear relationship was also found in the case of TiO2 NW aqueous suspensions. However, NWs preferred to settle parallel to the centrifugal direction under high RCF because of the lower flow resistance along the long axis. Thus, the extrapolated sedimentation velocity under regular gravity can be overestimated. Finally, a stable TiO2 NW suspension was formulated with a shear thinning fluid and showed great stability for weeks using visual observation. A theoretical analysis was deduced with rheological shear-thinning parameters to describe the nonlinear power-law dependence between the measured sedimentation velocities and RCF. The good agreement between the theoretical predictions and measurements suggested that the sedimentation velocity can be properly extrapolated to regular gravity. In summary, this accelerated assessment on a theoretical basis can yield quantitative information about long-term stability within a short time (a few hours) and can be further extended to other suspension systems.
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INTRODUCTION
However, because of the density difference between the dispersed nanomaterials and solvent, the gravitational force still results in inevitable sedimentation after long-term storage. For dilute particle suspension, the sedimentation velocity can be described by Stokes law as
The superior physical and chemical properties of nanostructured materials with respect to the conventional bulk materials have prompted extensive research of nanotechnology-based materials for next-generation products.1−5 To incorporate nanomaterials in thin film coatings or device fabrication, NPs or NWs are usually dispersed in liquid and applied to substrate surfaces by solution-based processes. However, stable suspensions with nanomaterials are difficult to formulate; the strong interactions between NPs or NWs lead to inevitable aggregation, which causes sediments, clogs in flow channels, and nonuniform thin films. Thus, the colloidal stability of a nanomaterial suspension is extremely important not only for the suspension shelf life but also for product quality. Typically, to formulate a well-stabilized NW suspension, the addition of surfactants and/or surface modifications of nanomaterials are regularly used to induce electrostatic or steric repulsion forces to counteract the attractive van der Waal forces between NPs or NWs and hence reduce agglomeration. © XXXX American Chemical Society
vs =
g (ρp − ρ)d p2 18μ
(1)
where g is the gravitational acceleration constant, ρp and ρ are the densities of the particle and fluid, respectively, dp is the particle size, and μ is the fluid viscosity. To slow down the gravitational sedimentation, one can disperse nanomaterials in a highly viscous fluid to produce a stable particle suspension for screen or gravure printing processes. However, in inkjet printing devices, Received: October 2, 2016 Revised: November 15, 2016 Published: November 22, 2016 A
DOI: 10.1021/acs.langmuir.6b03602 Langmuir XXXX, XXX, XXX−XXX
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Langmuir high-viscosity inks can lead to flow difficulties in microfluidic channels and thus decrease the printing speeds of inkjet printers. To maintain the fluidity of the suspension and to prevent sedimentation at the same time, recently Yang et al.6 formulated non-Newtonian fluids with didodecyldimethylammonium bromide (DDAB) vesicles to generate remarkably high shearthinning behavior and effectively stabilized TiO2 NPs from sedimentation. Because of the low viscosity under stress condition and extremely high viscosity under quiescence condition, this aqueous dispersion remains fluid in flow channels, and no sedimentation in the dispersion is observed after 6 months of storage. Owing to the unique one-dimensional nanostructure with a long aspect ratio, NWs have become promising candidates to produce flexible, transparent conductive thin films with great transparency and mechanical properties.7−9 To ensure the coating quality and to avoid troubles in coating processes, the colloidal stability of NW suspensions becomes a significant issue in these NW thin-film applications. However, these research studies focus primarily on material synthesis or coating processes for NWs rather than their colloidal stability.10−12 Moreover, most studies on colloidal stability focus mainly on NP dispersions.13−18 Thus, a systematic study on suspension stability is needed to evaluate the settling process of NWs in fluids. Despite the dispersion stability issues, traditional visual observation tests take a long time (more than 3 months) to assess the long-term stability of particular suspensions. In practice, a more time-saving or efficient dispersion stability analysis is required. Applications of centrifugal force to accelerate particle migration have been widely used in sedimentation tests and particle sizing.19−21 The analytical centrifuge can also be used to probe the sedimentation velocity of dispersions and thus provides a tool to calculate the shelf life of a product.22−24 In principle, the sedimentation velocity at earth’s gravity can be obtained by extrapolating measured velocities at different g values, or relative centrifugal forces (RCF), to regular gravity or 1 g.25 For spherical particles suspended in Newtonian fluids, a linear extrapolation can be obtained from Stokes’ law (eq 1). For non-Newtonian fluids, a nonlinear fitting equation of a power law type can also be deduced (and will be shown later).26 However, because NWs have two characteristic length dimensions, e.g., radius and length, the flow resistance can be very different from that of a spherical particle. It is invalid to directly apply the extrapolation method for spherical particles to NW suspension systems. Few researchers have studied the shape effects, such as disks or rodlike particles,27−31 on the settling velocity in Newtonian fluids. Thus, it might be worthwhile to extend the results from these studies to NW systems and validate the extended theorem experimentally for particle sedimentation in non-Newtonian fluids. In this work, TiO2 NWs are suspended in a non-Newtonian fluid to form a stable suspension. To quickly assess the long-term stability of this stable suspension, an analytical centrifuge is used to measure the sedimentation velocity of NWs at high RCF. The results will be carefully investigated to evaluate the validity of extrapolating the accelerated sedimentation velocity measurements at high RCF to regular gravity. The relationship of the sedimentation velocity of NWs in a non-Newtonian dispersion at high RCF will also be compared with the theoretical model to provide general guidelines for applying this extrapolation method for NWs in non-Newtonian fluids.
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and a bulk density of 4.25 g/cm3. TiO2 NW powder was purchased from Sigma-Aldrich. The nominal size is about 100 nm in diameter and 10 μm in length, and the density is 4.25 g/cm3. Didodecyldimethylammonium bromide (DDAB) was purchased from Sigma-Aldrich and used as received. Sample Preparation. A TiO2 NP or NW aqueous suspension was prepared by adding the powder to deionized water to a 0.1 wt % concentration. NPs suspensions were sonicated by an ultrasonic homogenizer (Ruptor 4000, Omni) with 50% (200 W) power output for 10 min in an ice bath. NW suspensions were sonicated by a homogenizer (Ruptor 4000, Omni) or in an ultrasonic bath (Delta DC300H) for 2 h to produce NW suspensions with different average lengths. The TiO2 aqueous suspensions with 2 wt % DDAB were prepared by adding an NW suspension to the DDAB powder and stirring for 1 h at 200 rpm. Sedimentation Velocity Measurements. Sedimentation velocities were measured by an analytical centrifugation analyzer, LUMisizer (LUM Corporation, CO). The device is equipped with a pulsed nearinfrared light-emitting diode (865 nm) as a light source and a chargecoupled device line with a spatial resolution of less than 10 μm as the light collector. Measurements were performed at 25 °C. In each measurement, 400 μL of the suspension was pipetted into a polycarbonate transparent cell with a 2 mm path length. Real-time transmission profiles across the sample were recorded at certain time intervals during centrifugation (Figure 1). The sedimentation velocity was determined
Figure 1. Schematic diagram of the sedimentation velocity prediction process with an analytical centrifuge, LUMisizer. The sedimentation progress is accelerated and recorded by the analytical centrifuge. Sedimentation velocities are measured by tracking the movements of the sedimentation boundary at the geometric average transmission. The long-term stability, or the sedimentation velocity under normal gravity, can be obtained by the extrapolation of the measured sedimentation velocities at high RCF to 1 g. by tracking the movements of the sedimentation boundary at the geometric mean value of the highest and lowest transmittance. Rheological Measurement. All rheological measurements were performed with a DV-III Ultra programmable rheometer (Brookfield) with a cone−plate spindle (CP52). The viscosities of Newtonian suspensions were measured at a shear rate of 100 s−1. At least three measurements were made for each sample. For non-Newtonian dispersions, the shear-rate-dependent viscosities were measured over a shear-rate range of 0.02 to 500 s−1. The shear rate swept from the highest value to the lowest and went back to the highest as a cycle. The average values of three measurements were reported.
EXPERIMENTAL SECTION
Materials. Titanium dioxide (P25) NP powder was obtained from UniRegion Bio-Tech. The particles have a nominal diameter of 21 nm B
DOI: 10.1021/acs.langmuir.6b03602 Langmuir XXXX, XXX, XXX−XXX
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Figure 2. Sedimentation velocity prediction for a 0.1 wt % TiO2 NP aqueous suspension. (a) Evolution of transmission profiles at 500 RCF. (b) Volumebased size distribution of the NP suspension. (c) Transient variation of the front position in panel a. The fitted straight line is determined as the sedimentation velocity. (d) Comparison of the measured sedimentation velocities and the theoretical values from Stokes’ law at different RCFs.
Figure 3. SEM images of dispersed NWs prepared by (a) bath sonication and (b) a homogenizer. (c, d) Length distributions determined by SEM examination of NWs in panels a and b, respectively. (e) Visual sedimentation test for the samples in panels a and b, as indicated in the picture.
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RESULTS AND DISCUSSION Sedimentation Velocity of a TiO2 NP Suspension. To validate the analytical centrifuge, the sedimentation velocities of a TiO2 NP suspension at high RCFs are first extrapolated to evaluate the stability at regular gravity. The transmission profiles across the sample chamber in the analytical centrifuge (LUMisizer)
are recorded at a given time step during centrifugation (Figure 2a). By tracking the front movements at a specific transmittance with time, one can easily determine the sedimentation velocity. Because of the polydispersity of the TiO2 NPs (Figure 2b), the geometric mean value28 of the transmission, according to Beer’s law,32 is used as the position of the boundary between concentrated C
DOI: 10.1021/acs.langmuir.6b03602 Langmuir XXXX, XXX, XXX−XXX
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Langmuir ⎛ ⎞ 1 1 1 2 = ⎜⎜ + ⎟⎟ fave 3⎝ f f⊥ ⎠
and supernatant phases to determine the volume-average sedimentation velocities. The front of the sediment is then tracked with time (Figure 2c), and the slope is calculated as the sedimentation velocity. As shown in Figure 2d, the sedimentation velocity increases linearly with the value of RCF, showing that the particle settling in this sample basically obeys Stokes’ law. Moreover, the measured sedimentation velocities at different RCF values are fairly close to the predicted sedimentation velocities based on Stokes’ law using the volume-average particle diameter (120 nm) measured by DLS. Therefore, sedimentation velocities measured at this standard can be quantitatively described by Stokes’ law and can be used to extrapolate the sedimentation velocity at regular gravity or 1 RCF. To simplify the analysis, the concentration of TiO2 is set in a dilute regime so that concentration effects can be neglected. The hydrodynamic interaction between particles or the so-called back-flow effect generally hinders particle settling. Batchelor33 found that the hindrance of spheres in a Newtonian fluid in the dilute regime is v = (1 − 6.55ϕ) v0 (2)
f =
1 fave
( l)
(5)
4πμL
( l)
ln 2 d + 0.19
(6)
where fave is the mean friction coefficient, V is the volume of an NW, d is the diameter of the rod, l is the rod length, and f∥ and f⊥ are the translational friction coefficients in directions parallel and perpendicular to the rod major axis, respectively. The sedimentation velocities of TiO2 NWs at various RCFs are summarized in Figure 4. TiO2 NWs with lengths of 0.76 and
where v0 is the sedimentation velocity at infinite dilution and ϕ is the volume fraction of particles. In this study, the volume fraction of a 0.1 wt % TiO2 NP suspension is about 0.00025, and the resulting hindrance is about 0.9984, meaning negligible backflow effects. As shown in Figure S1, the measured sedimentation velocity remains nearly the same regardless of concentration until 0.1 wt %, indicating the negligible effects of hindrance in this regime. On the other hand, the good agreement of the measured sedimentation velocities with Stokes’ law indicates that the extrapolated sedimentation velocity represents only the instability contribution from sedimentation. As a result, the diffusion of particles is neglected in these centrifugation tests. Because diffusion or the Brownian motion of particles tends to retain the concentration homogeneity of a suspension, the extrapolated sedimentation velocity via this method thus provides the fastest precipitation rate only for a long-term colloidal stability estimation. Sedimentation of an Aqueous Newtonian TiO2 NW Suspension. The longer dimension (>0.6 μm, Figure 3) of TiO2 NWs leads to faster sedimentation than for TiO2 NPs (∼120 nm) in water. The low stability of aqueous TiO2 NW suspensions against gravitational sedimentation can be easily observed by a simple visual observation (Figure 3e). The sedimentation begins within 2 days, and a clear liquid portion can be observed at the top. After a week, most of the NW precipitates at the bottom of the bottle. To further quantify the information about the colloidal stability of the NW suspension, the aforementioned analytical centrifuge method is applied. Because of the shape anisotropy, the flow resistance of a cylindrical particle is different from that of a spherical particle, especially cylinders with distinct orientations with respect to fluid motion. Theoretically, a long cylinder oriented parallel to the flow field moves faster than one perpendicular to the flow field. The drag forces on the cylinders can be derived analytically, and a long rod oriented parallel to the flow field moves faster than one perpendicular to the flow field. The average sedimentation velocity vs of a cylinder can be expressed by the mean friction coefficient as34 vs = g × RCF(ρp − ρ)V
2πμL ln 2 d − 0.81
f⊥ =
(4)
Figure 4. Sedimentation velocity of a 0.1 wt % TiO2 NW aqueous suspensions. The volume-averaged lengths of the NWs are (a) 6.03 and (b) 0.76 μm.
6.03 μm are tested at RCFs ranging from 30 to 1200. The measured sedimentation velocities of both NWs with different lengths show an obvious linear dependency on RCF, such as those observed in NP suspensions. The theoretical sedimentation velocities in eqs 3−6 are also calculated by using the volumeaverage length and diameter of NWs but have lower values than the measured velocities. Instead, the results are well-fitted when fave is replaced by f∥, indicating a strong dependence on NW orientation: NWs might align in the direction of the external centrifugal fields. Similar alignment phenomena are also reported by Hearst and Vinograd35 in measuring the sedimentation velocities of rodlike tobacco mosaic virus particles under centrifugal force. As a consequence, the measured sedimentation velocities of NWs under this analytical centrifuge method can be faster than those under regular gravity without flow directional preferences. Thus, although one can also extrapolate the measured velocities linearly as shown in eq 3 to probe the long-term stability for NW suspensions at regular gravity, the results might give an
(3) D
DOI: 10.1021/acs.langmuir.6b03602 Langmuir XXXX, XXX, XXX−XXX
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The linear dependence of sedimentation velocity on RCF no longer exists for the shear-dependent viscosity of a DDAB dispersion. In a power-law fluid, the settling velocity of an object can also be obtained from the force balance equation (eq 3). For a rod settling along its long axis (the preferred flow direction as shown previously), the flow resistance in eq 5 should be used with the non-Newtonian viscosity in eq 7. The resulting equation for the force balance equation (eq 3) becomes
overestimated value of the sedimentation velocity due to the preferred orientation of NWs under centrifugal fields. Sedimentation of a Non-Newtonian TiO2 NW Suspension. The stable non-Newtonian suspensions are prepared by mixing TiO2 NWs in the DDAB vesicle solution. TiO2 NWs suspended in this non-Newtonian solution becomes very stable (Figure 5). Compared to the counterpart aqueous TiO2 NW
vs = g × RCF(ρp − ρ)V
l ⎡ ⎤ ⎣ln 2 d − 0.81⎦
( )
2πKYγ ṅ − 1l
(8)
where Y is the drag correction factor accounting for nonNewtonian behaviors. The shear rate can be approximated as a ratio between the NW diameter and the sedimentation velocity:26 v γ̇ = s (9) d
Figure 5. Visual observation of the sedimentation of a 0.1 wt % TiO2 NW suspended in water (left) and an aqueous DDAB (right) dispersion.
suspensions in Figure 2, those NWs suspended in 2 wt % DDAB solution remain homogeneous without any observable sediments for weeks. By simple visual observation, DDAB vesicular dispersion does successfully prevent NWs from sedimentation; however, it takes a long time (a few weeks) to probe the stability, and an accelerated assessment by centrifugation is necessary. To exclude the possibility of NW inclusion in the vesicles, the rheological behaviors of the pure DDAB dispersion and the NW/ DDAB dispersion are first examined. As shown in Figure 6, the
By substituting eq 9 into eq 8 and rearrange the resulting equation, one obtains the sedimentation velocity as ⎧⎡ ⎫1/ n l ⎤ n+1 (ρp − ρ) ⎪ ⎣ln 2 d − 0.81⎦d ⎪ g × RCF⎬ vs = ⎨ 8 KY ⎪ ⎪ ⎩ ⎭
( )
(10)
The power-law relationship between vs and RCF in eq 10 now allows one to extrapolate the sedimentation velocity at regular gravity from the accelerated assessment. To verify the accelerated assessment for TiO2 NW sedimentation in the DDAB vesicular dispersion, the relationship between measured sedimentation velocities and RCF is investigated (Figure 7). The power-law index, n, and the flow con-
Figure 6. Variation of dispersion viscosity with shear rate. Here, a 2 wt % DDAB aqueous dispersion is used. The NW/DDAB dispersion is prepared by adding 0.1 wt % TiO2 NW (6 μm) to the DDAB solution. The supernatant of the NW/DDAB dispersion is obtained by centrifugation at 8832 RCF.
DDAB solution has a strong shear-thinning characteristic that is consistent with the literature.6 The shear stress τ and viscosity μ follow a power-law relation τ = Kγ ṅ = μγ ̇ or μ = Kγ ṅ − 1
Figure 7. Measured sedimentation velocities and the prediction for 0.1 wt % TiO2 NW in a 2 wt % aqueous DDAB dispersion.
(7)
where K is the flow consistency index, γ̇ is the shear rate, and n is the power-law index. After the addition of TiO2 NWs, the suspension remains shear thinning but with a slightly higher viscosity, possibly because of the addition of solid, as indicated by Bachelor.33 When the settling of NWs is accelerated by centrifugation, the stresses exerted on the vesicles by NWs can be amplified and might also result in broken vesicle structures. To test the strength of the DDAB vesicles, the NW suspension is centrifuged at 8832 RCF for 1 h to remove the NWs, and the supernatant clear solution is collected. The supernatant liquid after centrifugation exhibits almost the same shear-thinning behavior as the fresh DDAB solution, indicating that the vesicles remain intact during the NW sedimentation process or reform immediately after centrifugation.
sistency index, K, can be obtained from the rheological measurement (Figure S2 and Table S1). The shear rates for NW sedimentation under centrifugation can be roughly estimated by dividing measured sedimentation velocities by the diameter of nanowires, or eq 9. As shown in Figure S3, the power-law relationship holds well in the shear-rate range for NW sedimentation. The only unknown is the drag correction factor Y, which corresponds to the velocity fields around the settling object26 and varies with the aspect ratio of the NWs. However, without knowing the value of Y, one can find the measured values of vs is linearly dependent on RCF in a log−log plot as shown in Figure 7. The well-fitted result indicates the good agreement of NW sedimentation and the theoretical prediction, and thus one can extrapolate the results at high RCF to obtain the sedimentation E
DOI: 10.1021/acs.langmuir.6b03602 Langmuir XXXX, XXX, XXX−XXX
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velocity at regular gravity by using eq 10. Also, the value of parameter Y can be obtained from fitting the results in Figure 7 with eq 10. The values are 0.82 and 1.44 for short and long NWs, respectively, which are close to the ideal value of unity. The deviation may be attributed to non-Newtonian effects on the velocity fields, which relates to the power-law index and the shape of the object.26 The extrapolated sedimentation velocity at 1 g in the case of 6 μm NWs is extremely low at 8 × 10−11 (μm/s) or equivalently an overall traveling distance of 2 nm after 6 months. Such a virtually zero sedimentation velocity is actually due to vesicle blockage,6 which might also exhibit viscoelastic properties with some yield stress, and thus a good suspension stability can be achieved as observed in the visual test in Figure 5.
AUTHOR INFORMATION
ORCID
Ying-Chih Liao: 0000-0001-9496-4190 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
The authors are grateful for the financial support of this research from Ministry of Science and Technology (MOST) in Taiwan.
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CONCLUSIONS In this study, a stable TiO2 NW suspension is formulated with a non-Newtonian fluid and showed great stability for weeks. A simple and fast method is developed to quickly assess the longterm colloidal stability of the non-Newtonian NW suspensions. An analytical centrifuge is used to accelerate the sedimentation process and to measure the sedimentation velocities under high gravitational fields. The results can be extrapolated to provide an estimation for the sedimentation velocity at normal gravity. A validation test was provided by using a dilute aqueous TiO2 NP suspension. The results show that the measured sedimentation velocities via the analytical centrifuge are close to the theoretical values based on Stokes’ law. Similar accelerated assessments for TiO2 NW aqueous suspensions are also investigated to identify the flow resistance of the NWs in Newtonian fluids. The results also show a linear dependence of sedimentation velocity on RCF, indicating the feasibility of applying a centrifugal assessment to NW sedimentation. However, NW alignment occurs during sedimentation under high RCF because of the lower flow resistance in the long-axis direction. Thus, the extrapolated sedimentation velocity at regular gravity may underestimate the stability of the suspensions. Finally, the feasibility of this method for NWs stabilized in a shear-thinning power-law fluid is investigated. A theoretical analysis is deduced with rheological shear-thinning parameters to describe the nonlinear relationship between the measured sedimentation velocities and RCF. The good accordance between the theoretical prediction and measurements suggests that the extrapolated sedimentation velocity can properly represent the long-term colloidal stability of the NW/DDAB suspension. In summary, like suspensions with spherical particles, the accelerated assessment by centrifugation can be applied to NW suspensions to obtain quantified information about their long-term stability within a short time. The extrapolation method can also be applied to a non-Newtonian fluid via a nonlinear fitting process. This study provides a general guideline for suspension stability tests and can be further extended to other suspension systems.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b03602. Concentration effects on the sedimentation velocities. Best-fit power-law parameters of the NW/DDAB suspension. Comparison of the shear-rate ranges of rheological measurements of the NW/DDAB dispersion and the shear rates of NW sedimentation of nanowires under centrifugation. (PDF) F
DOI: 10.1021/acs.langmuir.6b03602 Langmuir XXXX, XXX, XXX−XXX
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