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Dispersion and rheology of nanofluids with various concentrations of organic modified nanoparticles: Modifier and solvent effects
Colloids and Surfaces A 583 (2019) 123876
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Dispersion and rheology of nanofluids with various concentrations of organic modified nanoparticles: Modifier and solvent effects
T
Muhammad Zamir Hossaina,b, Daisuke Hojoc, , Akira Yokod, , Gimyeong Seongc, Nobuaki Aokid, ⁎ Takaaki Tomaie, Seiichi Takamif, Tadafumi Adschiric,d,e, ⁎
⁎
a
Graduate School of Engineering, Tohoku University, 6-6 Aramaki Aza Aoba, Aoba-ku, Sendai 980-8579, Japan Department of Chemistry, Jagannath University, Dhaka, 1100, Bangladesh c New Industry Creation Hatchery Center, Tohoku University, 6-6-10 Aoba, Aramaki, Aoba-ku, Sendai, 980-8579, Japan d WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan e Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-2-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan f Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan b
GRAPHICAL ABSTRACT
ARTICLE INFO
ABSTRACT
Keywords: Nanofluids Rheology Organic modified nanoparticles Dispersibility Agglomeration Shear thinning/thickening
This article describes the relation between nanofluid viscosity and nanoparticle dispersibility. The rheological characteristics of dispersions of metal oxide nanoparticles was studied with covalently bonded organic molecules on their surfaces. Using a supercritical method, surface modification of the metal oxide nanoparticles with organic ligands was accomplished, thereby producing nanofluids of various kinds. By changing both the solvent and surface modifiers, the relation between the dispersive behavior and rheological characteristics of nanofluids was elucidated over widely various concentrations up to 30 vol.%. Then the nanofluid dispersibility was assessed in terms of their transparency, determined using ultraviolet – visible light spectroscopy, to correlate it to the nanofluid rheological behavior. Results reveal that transparent nanofluids behave as Newtonian fluids. Moreover, their relative viscosities converge to a certain viscosity range irrespective of the surface modifier and solvent type, whereas the non-transparent nanofluid viscosities are scattered above the transparent nanofluid viscosity range. After shear thinning, which is observed only for non-transparent nanofluids, the non-transparent nanofluid viscosity decreases and approaches the transparent nanofluid viscosity range. Furthermore, shear thickening occurs only at high nanoparticle concentrations of more than 23 vol.%, fundamentally independent of
⁎
Corresponding authors. E-mail addresses: [email protected] (D. Hojo), [email protected] (A. Yoko), [email protected] (T. Adschiri).
https://doi.org/10.1016/j.colsurfa.2019.123876 Received 28 May 2019; Received in revised form 16 August 2019; Accepted 27 August 2019 Available online 28 August 2019 0927-7757/ © 2019 Elsevier B.V. All rights reserved.
Colloids and Surfaces A 583 (2019) 123876
M.Z. Hossain, et al.
dispersibility. These findings provide a comprehensive picture of the relation between the nanofluid rheology and dispersive behavior, which is useful for nanofluid design.
1. Introduction
formation or deformation of flocculation of particles assisted by polymer bridging has been regarded as a cause of shear thickening or thinning. Different from a large particle system, dispersive behavior is important to understand the rheological characteristics of NFs. Contribution of the secondary structure of NPs (i.e., the aggregated structure) to non-Newtonian phenomena has been discussed for various NF systems [27–31]. However, most of the NF studies were limited to the low concentration range (0.01–10 vol.%) [32–34] and only a few articles have been reported for more than 10 vol.% [21,35] because of the instability of NFs, which results from the physically adsorbed surfactants or low coverage of modification. The rheological behavior of highly concentrated fluids with different affinities of NPs for solvents has not yet been elucidated. The effects of the structure (here, secondary structure or aggregation) on the property (here, viscosity) must be elucidated. This study used surface organic-ligand-modified CeO2 nanoparticles synthesized via a supercritical hydrothermal method as a model for investigation by changing the chain length of the surface modifiers. The rheological and dispersive behaviors of NFs was examined at widely various concentrations. The constituent solvents of the NFs were also changed to vary the NP–solvent interaction. The effects of the modifiers and solvents were specifically examined in this study. Other factors such as the temperature and the core particles were fixed. The NP dispersibility was evaluated in terms of the NF transparency using ultraviolet–visible (UV–vis) spectroscopy: the NF transparency is regarded as an index of the NP dispersibility because the formation of secondary structures (i.e., phase separation or aggregation) affects their transparency as a result of Rayleigh scattering. From the evaluated viscosity and dispersibility, the inclusive relation between the dispersive behaviors and rheological characteristics of NFs are examined using widely various NPs concentrations, which was not possible in earlier studies.
In most cases, nanoparticles (NPs) are used in a dispersed state to avoid their aggregation. Therefore, nanoparticle dispersibility is an important factor that must be considered for the efficient exploitation of their properties. In fact, the rheological behavior of nanoparticle dispersions is a key factor related to their handling. Recently, nanoparticle dispersions are attracting interest as nanofluids (NFs). Ideally, NFs can show the properties of both fluids and NPs, but it is difficult to realize such states. Increased concentration of NPs enhances the targeted property, but it usually inhibits their properties as fluids because of their increased viscosity. Concentrated NFs with low viscosity are necessary for various applications as heat transfer media [1,2] and nanoparticle transport media (e.g., drug delivery [3] and 3D printing [4]). In fact, designing NFs is necessary to support their use in various applications. Stabilizing nanoparticles that are dispersed in solvents requires some surface treatment of the nanoparticles themselves. Surface modification via covalent bonding is one important technique that has been achieved using a supercritical method [5–7] with organic molecules such as carboxylic acids. Small particles with a narrow size distribution have been created via in situ organic ligand modification of NPs during synthesis in supercritical water [8]. Because the surface properties of metal oxides can be tuned using organic modifiers, NFs of various kinds can be produced stably. Metal oxides are usually hydrophilic, but surface-modified NPs with hydrophobic modifiers can be dispersed well in non-polar organic solvents. High-density chemical bonds are formed between the modifiers and the metal oxide particle surfaces. Moreover, the modifier layer is stable at temperatures as high as 400 °C because of the strong chemical bonding which occurs at the surface [9]. The NP agglomeration has been demonstrated as suppressed up to the markedly high concentration of 77 wt.% [10,11]. Consequently, because of advances in organic modification techniques with supercritical water, it is possible to evaluate NF properties at widely various concentrations. In addition, the interactions of surface modifiers and solvents, which might be determinant factors of NFs, can be changed by altering the size of the modifier molecules. Earlier rheological studies of NFs have mainly examined the effects of particle size, particle shape, temperature, stabilizer types, and volume fractions of NPs [12–21]. In other studies, NFs were observed to be Newtonian fluids or non-Newtonian fluids, which show shear thickening [22–24] or shear thinning [21,25,26] phenomena, depending on their conditions. Transitions from Newtonian to shearthinning or shear-thickening fluids at a certain shear rate that depends on the concentration and particle size have been observed. In fact, the
2. Experimental 2.1. Materials Cerium (IV) hydroxide (Aldrich Chemical Co. Inc., USA) was used as a starting material of NPs. Surface modifiers such as octanoic acid (99%), decanoic acid (99%), octadecanoic (stearic) acid (99.5%) were used. Organic solvents such as ethanol (99%), cyclohexane (99.5%), nhexane (96%), acetone (99%), dodecane (99%), and trans-decahydronaphthalene (decalin, 97%) were used (Fujifilm Wako Pure Chemical Corp.). Purified water was obtained from Daiwa Pharmaceutical Co. Ltd.
Fig. 1. TEM images of the synthesized CeO2 NPs surface-modified with (A) octanoic acid (C8), (B) decanoic acid (C10), and (C) stearic acid (C18). White scale bars in the images represent 50 nm. 2
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Fig. 2. Particle size distributions of synthesized CeO2 NPs obtained from TEM images measuring 300 particles, surface modified with (A) octanoic acid (C8), (B) decanoic acid (C10), and (C) stearic acid (C18).
2.2. NP synthesis
calculated because the physical state and the density of modifiers change with respect to their original state of free molecules.
Surface organic modified CeO2 NPs were synthesized from cerium hydroxide. The precursor was a 0.1 mol/L aqueous suspension of Ce (OH)4, which was prepared by adding 0.229 g of Ce(OH)4 to 11 mL of deionized water, with ultrasonication for 10 s. The precursor (2.5 mL) was loaded into a batch reactor (5 mL inner volume, Hastelloy C). The molar ratio of cerium to modifier was set as 1: 3 for NP surface modification. As modifiers, straight-chain carboxylic acids with different chain lengths were used: octanoic acid (C8), decanoic acid (C10), and stearic acid (C18). Two-step hydrothermal reactions were conducted using two electric furnaces. The first step was pretreatment at 150 °C for 20 min. The second step was a reaction conducted at 400 °C for 10 min. The reaction was terminated by submerging the reactor into a water bath. Then the products were collected with 5 mL of n-hexane. The organic phase, in which surface-modified NPs exist, was recovered. The unreacted organic fatty acids were removed by centrifugation at 9600 rpm for 20 min with ethanol. For further purification, products were re-dispersed in cyclohexane and were added dropwise to acetone (cyclohexane: acetone = 1: 20 of volume ratio) with magnetic stirring, followed by centrifugation at 9600 rpm for 20 min. This step was repeated three times to remove all unreacted modifiers. Centrifuged particles were dispersed in cyclohexane and were kept overnight to ensure that they were well dispersed. Then, the upper layer of the dispersion that contains well-dispersed NPs was collected and freezedried under vacuum until all cyclohexane was removed. The products modified by C8, C10, and C18 were labeled respectively as C8–CeO2, C10–CeO2, and C18–CeO2.
2.4. NP characterization The particle size and morphology of the NPs were examined using transmission electron microscopy (TEM, H–7650; Hitachi Corp., Japan) with 100 kV acceleration voltage. The mean particle size and the standard deviation were obtained by measuring 300 particles in the TEM images. The amounts of organic modifiers attached to the NP surface were measured using thermogravimetric analysis (TG, DTG60AH; Shimadzu Corp., Japan) under a N2 gas flow atmosphere (100 mL/min) at temperatures from room temperature to 800 °C at a heating rate of 10 °C/min. The modifier coverage ([(the number of molecules) nm−2]) on the NP core surface was estimated from the average NP core size measured using TEM and the amounts of modifiers measured using TG analysis. 2.5. NF characterization The NF transparency was characterized using a UV–vis spectrophotometer (V-570 UV/VIS/NIR; Jasco Inc., Japan). All the UV–vis measurements were taken at 20 °C using a quartz cell with 1 mm path length. The NFs of this study were stable. No apparent change was observed. The NF viscosity was measured using a programmable rotational rheometer (LVDV–III Ultra; Brookfield Engineering, USA). The spindle and plate sections were used with a cone–plate geometry to obtain uniform shear. Here, the viscosity is the ratio of shear stress to shear rate: η = σ/γ, with viscosity η, shear rate γ, and shear stress σ. Fluids are classifiable into three types with the shear rate dependence of viscosity: as Newtonian (constant viscosity with shear rate), shear-thinning (decreasing viscosity with increased shear rate), and shear-thickening (increasing viscosity with increased shear rate). Experiments were conducted using spindles CPE-40 (2.4 cm cone radius) and CPE-51
2.3. NF preparation After the freeze-dried surface-modified NPs were recovered, their weight was measured using a sensitive electronic balance (AUW120D; Shimadzu Corp.) with accuracy of 0.1 mg. The NPs were added to organic solvents such as cyclohexane, trans-decahydronaphthalene (decalin), and dodecane (0.5–1.0 mL) and were mixed by manual shaking with no mechanical treatment. The NFs were prepared with weight percent, φ (wt%), concentration. The corresponding total volume fraction Φ (vol.%) was calculated based on TG weight loss x with the following equations:
(wt%) =
M × 100 M + Msol Mcore
(vol%) =
core
Mcore core
+
+
(1)
Mmod
Mmod mod
mod
+ Vsol
(1
× 100 =
x)M core
(1
x) M core
+
+
xM mod
xM mod
Vsol
× 100 (2)
where M represents the mass of the surface-modified CeO2 NPs, Msol denotes the solvent mass, Mcore stands for the particle core mass, Mmod represents the mass of the modifier-attached particle, ρmod denotes the modifier density, ρmod signifies the core density, and Vsol expresses the solvent volume. The density of modifiers on the particle surface was
Fig. 3. TG-weight loss of surface modifiers on NPs under N2 atmosphere at a heating rate of 10 °C/min: (A) C8–CeO2, (B) C10–CeO2, and (C) C18–CeO2. 3
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Table 1 Modified state of the NPs (C8-CeO2, C10-CeO2, and C18-CeO2) used to prepare NFs based on TEM and TG-DTA analysis. NPs
C8-CeO2
C10-CeO2
C18-CeO2
Particle size (TEM) [nm] TGA weight loss fraction, x [-] Modifier coverage [(number of molecules) nm−2] Thickness of the modifier layer, T [nm] Density of free modifier molecules [g cm−3] Modifier density on particle surface, ρmod [g cm−3]
6.0 ± 1.0 0.12 3.9 0.87 0.910 1.08
7.0 ± 0.8 0.14 4.7 1.07 0.893 1.25
6.6 ± 1.8 0.21 4.5 1.90 0.847 1.12
200 s−1. Data obtained at higher shear rate conditions of 200–1200 s−1 were used for analysis.
(1.2 cm cone radius) depending on the NF amount. The cell temperature was maintained at 20 °C during all viscosity measurements. Each measurement point was obtained after 60 s of achieving constant shear rates on the samples. The measurements were repeated five times for each sample. Deviation of the measured viscosity at the same shear rate converged to less than ± 1.0% for all samples under the condition that the shear rate is higher than 200 s−1. Stable conditions with error in viscosity of less than 1.0% were achieved with a shear rate higher than
3. Results and discussion 3.1. NP surface properties The modifier coverage, which is defined as the number of bound
Fig. 4. UV–vis spectra of NFs composed of CeO2 NPs at different volume fractions: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/dodecane. (E) Volume fraction dependence of the absorbance at 800 nm wavelength. The linear relation between the absorbance (log10 (I0/I)) and log10Φ reflects the dispersed state. The sudden jump in the absorbance shows the initiation of the agglomeration of NPs. This change is used to identify NF with the maximum volume fraction retaining its dispersibility. 4
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modifiers per unit of surface area on the core particle surface, is an important factor affecting surface-modified NPs in terms of their dispersibility in solvents. At a higher modifier coverage, NPs can be hydrophobic [10,11]. The modifier coverage is calculable from the weight loss occurring during TG analysis and the size of the core particles as determined using TEM. Figs. 1(A)–(C) portray TEM images of CeO2 NPs with different modifiers. Figs. 2(A)–(C) show the particle size distributions obtained from TEM images. The results reveal that all the surface-modified CeO2 NPs have small core (CeO2) size of approximately 7 nm with a narrow monodispersed size distribution. Fig. 3 shows TG curves of the respective surface-modified NP samples. A gradual decrease in weight loss was observed at temperatures of 300–700 °C for all samples. Actually, the TG weight loss in this temperature range, which is higher than the boiling points of modifier molecules, indicates that the organic modifiers are not physically absorbed but are in fact chemically bonded to the NP surfaces [9]. The TG weight loss, which is attributed to the thermal decomposition of organic molecules in the products, reflects the number of surface modifiers on NP surfaces. The calculated modifier coverage on the CeO2 particles is quite high, as shown in Table 1. The maximum theoretical modifier coverage of surface modifiers on the metal oxide surface has been reported as 5.3 molecules nm−2 based on the cross-sectional area of an alkyl chain [36]. For comparison, the number of surface cerium atoms is 6.8 nm−2 at the (100) surface of CeO2. As might be readily apparent from Table 1, the calculated densities of modifiers are 19–40% higher than those in the original state at room temperature because of the high-packing structures of the modifiers and because of their alignment. These results, regarded in light of an earlier study [36], suggest that the modifiers are densely packed and nearly vertically oriented as quasicrystalline structures. This unique feature of surface modified NPs, where dense organic layers were formed on the NP surfaces, contributed to the high affinity of hybrid NPs to nonpolar solvents such as cyclohexane and the formulation of stable concentrated NFs. The volume fractions (Φ [vol.%]) of the CeO2 NFs were calculated based on the TEM and TG data. The values used for calculations are presented in Table 1. It is noteworthy that the estimated ρmod, the density of the organic modifiers bound to the surface of the cores, differs from the value found in their original states as free molecules, as explained above.
Table 2 Maximum volume fraction of transparent NFs found using UV–vis spectroscopy (shown in Fig. 3). Type of NF
Maximum Φ (vol.%) with transparency
C10-CeO2/cyclohexane C18-CeO2/cyclohexane C8-CeO2/decalin C10-CeO2/dodecane
23.3 0.2 1.0 0.1
absorbance is used as a criterion in this study to distinguish between transparent (dispersive) and opaque (agglomerative) NFs, as presented in Fig. 4(E). The limit of the volume fraction for obtaining transparent NFs was found using UV–vis spectroscopy (Fig. 4(E)). The determined values for each NF are presented in Table 2. Photographs of the four transparent NFs with the highest probable volume fraction and the volume fraction at which the NPs start to agglomerate are presented in Fig. 5. The NFs
3.2. NF dispersibility For this study, four types of CeO2 NFs with different modifiers in different solvents were prepared at various concentrations: C8–CeO2/ decalin, C10–CeO2/cyclohexane, C10–CeO2/dodecane, and C18–CeO2/ cyclohexane. Depending on the modifier–solvent affinity, the maximum volume fractions of NFs with completely dispersed particles differ with different combinations. When the NPs are dispersed completely, NPs exist as single particles in the solvent. Such NFs are transparent to visible light because the NPs are much smaller than the wavelength of visible light: Mie scattering does not occur. In fact, the NFs remain transparent until the NPs start to agglomerate to sizes comparable to visible light wavelengths. Agglomeration, i.e., the formation of secondary structures, was observed using UV–vis spectroscopy. Fig. 4(A)–(D) show the absorption spectra of the four NFs. Here, absorbance is defined as log10 (I0/I), where I0 and I respectively represent the intensities of the incident and transmission light. An increase in absorbance is observed with increase in the NP volume fraction of all NFs. Fig. 4(E) shows the volume fraction dependence of the absorbance at 800 nm for each NF, where Rayleigh scattering is expected and solvents have no absorption. The absorbance values at 800 nm increased with an increase in the volume fraction. However, no linear correlation with NP concentration, which is expected for complete dispersions, is observed for NFs in the high concentration range. The sharp increase in the absorbance suggests the agglomeration of NPs to structures with sizes on the order of hundreds of nanometers. The abrupt change in
Fig. 5. Photographs of NFs of four types with the highest concentration maintaining transparency (left column) and that of starting agglomeration (right column) evaluated using UV–vis spectroscopy: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/ dodecane. Numbers on the images show the volume fraction of each NF. 5
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Fig. 6. Viscosities of transparent NFs evaluated using UV–vis spectroscopy at different volume fractions as a function of the shear rate: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/dodecane.
Fig. 7. Viscosity of non-transparent NFs evaluated using UV–vis spectroscopy at different volume fractions as a function of the shear rate: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/dodecane.
6
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classified via UV–vis analysis as complete dispersions also appear transparent in the images. The threshold volume fraction to obtain a transparent NF differs significantly for NFs of different types. For example, C10–CeO2/cyclohexane NFs remained transparent even at volume fractions as high as 23.3 vol.%. By contrast, C10–CeO2/dodecane NFs appeared agglomerated at 0.1 vol.%. The rheological characteristics of the NFs are analyzed in the following section based on dispersibility evaluated in this section. 3.3. Viscosity of dispersed NFs The viscosities of NFs with various volume fractions of NPs were measured by varying the shear rates. The NF viscosities are discussed based on the NF classifications presented in the previous section. Fig. 6 shows the rheological behaviors of dispersed NFs: most viscosities of the transparent NFs are low and independent of the shear rate, i.e., Newtonian fluids, irrespective of the modifier and solvent types. The only exception is the dispersed C10–CeO2/cyclohexane at 23.3 vol.%. Its viscosity increased with an increase in the shear rate, as shown in Fig. 6(A): it showed shear thickening behavior. That shear thickening behavior is visible irrespective of the dispersive behavior, as explained later. Except for the shear thickening cases, all the transparent or dispersive NFs are Newtonian fluids. 3.4. Viscosity of agglomerated NFs All the agglomerated NFs exhibited higher viscosities than those of the dispersed NFs. In contrast to the dispersed NFs, shear thinning behavior was observed in addition to Newtonian and shear thickening behavior in the case of agglomerated NFs. Shear thickening behavior was observed at high concentration ranges such as 29.4 vol.% for C10–CeO2/cyclohexane NF and 31.6 vol.% for C8–CeO2/decalin NF, as presented in Fig. 7(A) and (C). Shear thickening is observed in both dispersed and agglomerated NFs. However, the volume fraction range is limited to highly concentrated conditions: higher than approximately 23 vol.%. Results show that the origin of shear thickening is not the initial agglomeration but rather the high concentration. Some structures might form under shear at high concentrations irrespective of the initial dispersibility before shear applications. The NFs agglomerated at low concentrations such as 1.2 vol.% of C18–CeO2/cyclohexane and 0.2 vol.% of C10–CeO2/dodecane show Newtonian behavior, as presented in Fig. 7(B) and (D). An increase in the NP concentration caused clear shear thinning, as shown in Fig. 7(B)–(D), which is not observed in the case of the transparent NFs. The shear thinning behavior was observed only in the case of agglomerated NFs. Thereby, the origin of shear thinning can be attributed to agglomeration size of several hundred nanometers. Such agglomeration depends on the NP concentration and the affinity of NPs and solvents.
Fig. 8. Relative viscosity of NFs as a function of volume fraction of NPs: (A) Viscosity at the shear rate of 200 s−1, with plots unfilled showing dispersed NFs and plots filled showing agglomerated NFs. (B) After the application of shear force (the viscosity at the highest applied shear rates for each NF), with blue plots showing Newtonian, red plots showing shear thinning, and yellow plots showing shear thickening. For both (A) and (B), the solid line represents the Einstein model for low concentration; the dotted line shows the Happel model for high concentration. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
shear thickening), the relative viscosity at a shear rate of 200 s−1 is shown in Fig. 8(A). The relations between the relative viscosity and the volume fraction given by the Einstein viscosity equation for the low volume fraction suspension [40] and the Happel cell model [41] developed for highly concentrated fluids are presented in Fig. 8. The viscosity of each dispersed NF increased monotonically with the increase in the volume fraction, irrespective of the type of solvent. Then they are well-understood by these conventional models, as shown in Fig. 8. In contrast, the relative viscosity of the agglomerated NFs is scattered above the viscosities of the dispersed NFs. Even at equal concentrations, the viscosities of the agglomerated NFs are much higher than those of the dispersed NFs. The viscosity of some of the agglomerated NFs did not simply increase with an increase in the volume fraction of NPs, as shown in Fig. 8(A). The viscosities of the agglomerated NFs were apparently determined not only by their volume fractions. They were also affected by the degree of agglomeration. Fig. 8(B) portrays the volume fraction dependence of the relative viscosities at the highest applied shear rate for each NF. The final
3.5. Relation between viscosity and dispersibility The relative viscosities of the NFs (i.e., the ratios of the apparent viscosity of the NF to the viscosity of the solvent, r = NF / solv ) were calculated for comparison. The viscosities of solvents such as cyclohexane, decalin, and dodecane are independent of the shear rate: they are Newtonian fluids. The average viscosity values of cyclohexane (0.86 mPa·s), decalin (2.05 mPa·s), and dodecane (1.42 mPa·s) at 20 °C are consistent with the values reported earlier in the relevant literature [37–39]. Fig. 8(A) shows the relation between the relative viscosity and volume fraction of the NFs: unfilled symbols represent transparent NFs; filled symbols represent non-transparent NFs. The apparent viscosity of the Newtonian NFs was found from the slope of the shear rate vs. shear stress curve. These values were used to calculate the relative viscosity. For shear-dependent NFs (non-Newtonian; both shear thinning and 7
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apparent viscosity at the highest applied shear rate was used to calculate the relative viscosity for the shear-dependent non-Newtonian NFs. The symbols in Fig. 8(B) are blue for Newtonian fluids, red for shear thinning fluids, and yellow for shear thickening fluids. Under the application of shear stress to these agglomerated NFs, their viscosity decreased and approached the viscosity range of the transparent NFs, as shown in Fig. 8(b), suggesting that the deformation of agglomeration initially exists in non-transparent NFs. The initial agglomerated structure of NPs in these non-transparent NFs was possibly broken down by shear stress, similarly to behaviors found in studies reported earlier [25,26,42]. The viscosity of some of the agglomerated NFs remained higher than that of the dispersed NFs in Fig. 8(b), indicating that the NPs persistently agglomerated even under shearing force and indicating that the remnant agglomerates contributed to the increased viscosity of these NFs. At very high concentrations, NFs exhibit shear thickening irrespective of the initial dispersibility evaluated via UV–vis. Indeed, at concentrations greater than approx. 23 vol.%, C10–CeO2/cyclohexane (dispersed) and C8–CeO2/decalin (agglomerated) NFs showed shear thickening behavior, as denoted by yellow symbols in Fig. 8(B). Shear thickening was observed sometimes for concentrated NFs in which the NPs are self-organized under shear stress [43–45], probably because the average distance between the NPs is comparable to the size of NPs, i.e., the distance can be in the range of the potential curve between NPs [46,47].
[3] [4]
[5] [6]
[7] [8] [9] [10] [11]
[12]
4. Conclusions
[13]
Rheological behavior such as Newtonian behavior, shear thinning, and shear thickening was classified with dispersive behavior measured using UV–vis spectroscopy over widely various concentrations while controlling the affinity of NPs and solvents by changing organic modifiers. At lower concentrations (approximately less than 23 vol%), the relative viscosities of dispersive NFs show Newtonian behavior irrespective of the solvents or surface modifiers used. Shear thinning occurred only for non-dispersive NFs. After shear thinning, the viscosity approached the viscosity range of Newtonian NFs. Agglomeration of several hundred nanometers’ size and de-agglomeration by shear application are attributed to shear thinning. By contrast, shear thickening occurs in both dispersed and agglomerated NFs, but only in highly concentrated NFs of more than 23 vol.%. The origin of shear thickening is not the initial agglomeration but the structural formation of NPs under shear at high NP concentrations.
[14] [15] [16]
[17]
[18]
[19]
Declaration of Competing Interest [20]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[21]
Acknowledgments
[22]
This work was supported by JSPS KAKENHI Grants (Nos. JP 25249108, 16H06367), SIP Project, “Innovative design/manufacturing technologies on-demand on 3D additive manufacturing of structural functional materials and 3D devices through the creation of fluidic material”, the World Premier International Research Centre Initiative (WPI), and the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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Colloids and Surfaces A journal homepage: www.elsevier.com/locate/colsurfa
Dispersion and rheology of nanofluids with various concentrations of organic modified nanoparticles: Modifier and solvent effects
T
Muhammad Zamir Hossaina,b, Daisuke Hojoc, , Akira Yokod, , Gimyeong Seongc, Nobuaki Aokid, ⁎ Takaaki Tomaie, Seiichi Takamif, Tadafumi Adschiric,d,e, ⁎
⁎
a
Graduate School of Engineering, Tohoku University, 6-6 Aramaki Aza Aoba, Aoba-ku, Sendai 980-8579, Japan Department of Chemistry, Jagannath University, Dhaka, 1100, Bangladesh c New Industry Creation Hatchery Center, Tohoku University, 6-6-10 Aoba, Aramaki, Aoba-ku, Sendai, 980-8579, Japan d WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan e Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-2-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan f Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan b
GRAPHICAL ABSTRACT
ARTICLE INFO
ABSTRACT
Keywords: Nanofluids Rheology Organic modified nanoparticles Dispersibility Agglomeration Shear thinning/thickening
This article describes the relation between nanofluid viscosity and nanoparticle dispersibility. The rheological characteristics of dispersions of metal oxide nanoparticles was studied with covalently bonded organic molecules on their surfaces. Using a supercritical method, surface modification of the metal oxide nanoparticles with organic ligands was accomplished, thereby producing nanofluids of various kinds. By changing both the solvent and surface modifiers, the relation between the dispersive behavior and rheological characteristics of nanofluids was elucidated over widely various concentrations up to 30 vol.%. Then the nanofluid dispersibility was assessed in terms of their transparency, determined using ultraviolet – visible light spectroscopy, to correlate it to the nanofluid rheological behavior. Results reveal that transparent nanofluids behave as Newtonian fluids. Moreover, their relative viscosities converge to a certain viscosity range irrespective of the surface modifier and solvent type, whereas the non-transparent nanofluid viscosities are scattered above the transparent nanofluid viscosity range. After shear thinning, which is observed only for non-transparent nanofluids, the non-transparent nanofluid viscosity decreases and approaches the transparent nanofluid viscosity range. Furthermore, shear thickening occurs only at high nanoparticle concentrations of more than 23 vol.%, fundamentally independent of
⁎
Corresponding authors. E-mail addresses: [email protected] (D. Hojo), [email protected] (A. Yoko), [email protected] (T. Adschiri).
https://doi.org/10.1016/j.colsurfa.2019.123876 Received 28 May 2019; Received in revised form 16 August 2019; Accepted 27 August 2019 Available online 28 August 2019 0927-7757/ © 2019 Elsevier B.V. All rights reserved.
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dispersibility. These findings provide a comprehensive picture of the relation between the nanofluid rheology and dispersive behavior, which is useful for nanofluid design.
1. Introduction
formation or deformation of flocculation of particles assisted by polymer bridging has been regarded as a cause of shear thickening or thinning. Different from a large particle system, dispersive behavior is important to understand the rheological characteristics of NFs. Contribution of the secondary structure of NPs (i.e., the aggregated structure) to non-Newtonian phenomena has been discussed for various NF systems [27–31]. However, most of the NF studies were limited to the low concentration range (0.01–10 vol.%) [32–34] and only a few articles have been reported for more than 10 vol.% [21,35] because of the instability of NFs, which results from the physically adsorbed surfactants or low coverage of modification. The rheological behavior of highly concentrated fluids with different affinities of NPs for solvents has not yet been elucidated. The effects of the structure (here, secondary structure or aggregation) on the property (here, viscosity) must be elucidated. This study used surface organic-ligand-modified CeO2 nanoparticles synthesized via a supercritical hydrothermal method as a model for investigation by changing the chain length of the surface modifiers. The rheological and dispersive behaviors of NFs was examined at widely various concentrations. The constituent solvents of the NFs were also changed to vary the NP–solvent interaction. The effects of the modifiers and solvents were specifically examined in this study. Other factors such as the temperature and the core particles were fixed. The NP dispersibility was evaluated in terms of the NF transparency using ultraviolet–visible (UV–vis) spectroscopy: the NF transparency is regarded as an index of the NP dispersibility because the formation of secondary structures (i.e., phase separation or aggregation) affects their transparency as a result of Rayleigh scattering. From the evaluated viscosity and dispersibility, the inclusive relation between the dispersive behaviors and rheological characteristics of NFs are examined using widely various NPs concentrations, which was not possible in earlier studies.
In most cases, nanoparticles (NPs) are used in a dispersed state to avoid their aggregation. Therefore, nanoparticle dispersibility is an important factor that must be considered for the efficient exploitation of their properties. In fact, the rheological behavior of nanoparticle dispersions is a key factor related to their handling. Recently, nanoparticle dispersions are attracting interest as nanofluids (NFs). Ideally, NFs can show the properties of both fluids and NPs, but it is difficult to realize such states. Increased concentration of NPs enhances the targeted property, but it usually inhibits their properties as fluids because of their increased viscosity. Concentrated NFs with low viscosity are necessary for various applications as heat transfer media [1,2] and nanoparticle transport media (e.g., drug delivery [3] and 3D printing [4]). In fact, designing NFs is necessary to support their use in various applications. Stabilizing nanoparticles that are dispersed in solvents requires some surface treatment of the nanoparticles themselves. Surface modification via covalent bonding is one important technique that has been achieved using a supercritical method [5–7] with organic molecules such as carboxylic acids. Small particles with a narrow size distribution have been created via in situ organic ligand modification of NPs during synthesis in supercritical water [8]. Because the surface properties of metal oxides can be tuned using organic modifiers, NFs of various kinds can be produced stably. Metal oxides are usually hydrophilic, but surface-modified NPs with hydrophobic modifiers can be dispersed well in non-polar organic solvents. High-density chemical bonds are formed between the modifiers and the metal oxide particle surfaces. Moreover, the modifier layer is stable at temperatures as high as 400 °C because of the strong chemical bonding which occurs at the surface [9]. The NP agglomeration has been demonstrated as suppressed up to the markedly high concentration of 77 wt.% [10,11]. Consequently, because of advances in organic modification techniques with supercritical water, it is possible to evaluate NF properties at widely various concentrations. In addition, the interactions of surface modifiers and solvents, which might be determinant factors of NFs, can be changed by altering the size of the modifier molecules. Earlier rheological studies of NFs have mainly examined the effects of particle size, particle shape, temperature, stabilizer types, and volume fractions of NPs [12–21]. In other studies, NFs were observed to be Newtonian fluids or non-Newtonian fluids, which show shear thickening [22–24] or shear thinning [21,25,26] phenomena, depending on their conditions. Transitions from Newtonian to shearthinning or shear-thickening fluids at a certain shear rate that depends on the concentration and particle size have been observed. In fact, the
2. Experimental 2.1. Materials Cerium (IV) hydroxide (Aldrich Chemical Co. Inc., USA) was used as a starting material of NPs. Surface modifiers such as octanoic acid (99%), decanoic acid (99%), octadecanoic (stearic) acid (99.5%) were used. Organic solvents such as ethanol (99%), cyclohexane (99.5%), nhexane (96%), acetone (99%), dodecane (99%), and trans-decahydronaphthalene (decalin, 97%) were used (Fujifilm Wako Pure Chemical Corp.). Purified water was obtained from Daiwa Pharmaceutical Co. Ltd.
Fig. 1. TEM images of the synthesized CeO2 NPs surface-modified with (A) octanoic acid (C8), (B) decanoic acid (C10), and (C) stearic acid (C18). White scale bars in the images represent 50 nm. 2
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Fig. 2. Particle size distributions of synthesized CeO2 NPs obtained from TEM images measuring 300 particles, surface modified with (A) octanoic acid (C8), (B) decanoic acid (C10), and (C) stearic acid (C18).
2.2. NP synthesis
calculated because the physical state and the density of modifiers change with respect to their original state of free molecules.
Surface organic modified CeO2 NPs were synthesized from cerium hydroxide. The precursor was a 0.1 mol/L aqueous suspension of Ce (OH)4, which was prepared by adding 0.229 g of Ce(OH)4 to 11 mL of deionized water, with ultrasonication for 10 s. The precursor (2.5 mL) was loaded into a batch reactor (5 mL inner volume, Hastelloy C). The molar ratio of cerium to modifier was set as 1: 3 for NP surface modification. As modifiers, straight-chain carboxylic acids with different chain lengths were used: octanoic acid (C8), decanoic acid (C10), and stearic acid (C18). Two-step hydrothermal reactions were conducted using two electric furnaces. The first step was pretreatment at 150 °C for 20 min. The second step was a reaction conducted at 400 °C for 10 min. The reaction was terminated by submerging the reactor into a water bath. Then the products were collected with 5 mL of n-hexane. The organic phase, in which surface-modified NPs exist, was recovered. The unreacted organic fatty acids were removed by centrifugation at 9600 rpm for 20 min with ethanol. For further purification, products were re-dispersed in cyclohexane and were added dropwise to acetone (cyclohexane: acetone = 1: 20 of volume ratio) with magnetic stirring, followed by centrifugation at 9600 rpm for 20 min. This step was repeated three times to remove all unreacted modifiers. Centrifuged particles were dispersed in cyclohexane and were kept overnight to ensure that they were well dispersed. Then, the upper layer of the dispersion that contains well-dispersed NPs was collected and freezedried under vacuum until all cyclohexane was removed. The products modified by C8, C10, and C18 were labeled respectively as C8–CeO2, C10–CeO2, and C18–CeO2.
2.4. NP characterization The particle size and morphology of the NPs were examined using transmission electron microscopy (TEM, H–7650; Hitachi Corp., Japan) with 100 kV acceleration voltage. The mean particle size and the standard deviation were obtained by measuring 300 particles in the TEM images. The amounts of organic modifiers attached to the NP surface were measured using thermogravimetric analysis (TG, DTG60AH; Shimadzu Corp., Japan) under a N2 gas flow atmosphere (100 mL/min) at temperatures from room temperature to 800 °C at a heating rate of 10 °C/min. The modifier coverage ([(the number of molecules) nm−2]) on the NP core surface was estimated from the average NP core size measured using TEM and the amounts of modifiers measured using TG analysis. 2.5. NF characterization The NF transparency was characterized using a UV–vis spectrophotometer (V-570 UV/VIS/NIR; Jasco Inc., Japan). All the UV–vis measurements were taken at 20 °C using a quartz cell with 1 mm path length. The NFs of this study were stable. No apparent change was observed. The NF viscosity was measured using a programmable rotational rheometer (LVDV–III Ultra; Brookfield Engineering, USA). The spindle and plate sections were used with a cone–plate geometry to obtain uniform shear. Here, the viscosity is the ratio of shear stress to shear rate: η = σ/γ, with viscosity η, shear rate γ, and shear stress σ. Fluids are classifiable into three types with the shear rate dependence of viscosity: as Newtonian (constant viscosity with shear rate), shear-thinning (decreasing viscosity with increased shear rate), and shear-thickening (increasing viscosity with increased shear rate). Experiments were conducted using spindles CPE-40 (2.4 cm cone radius) and CPE-51
2.3. NF preparation After the freeze-dried surface-modified NPs were recovered, their weight was measured using a sensitive electronic balance (AUW120D; Shimadzu Corp.) with accuracy of 0.1 mg. The NPs were added to organic solvents such as cyclohexane, trans-decahydronaphthalene (decalin), and dodecane (0.5–1.0 mL) and were mixed by manual shaking with no mechanical treatment. The NFs were prepared with weight percent, φ (wt%), concentration. The corresponding total volume fraction Φ (vol.%) was calculated based on TG weight loss x with the following equations:
(wt%) =
M × 100 M + Msol Mcore
(vol%) =
core
Mcore core
+
+
(1)
Mmod
Mmod mod
mod
+ Vsol
(1
× 100 =
x)M core
(1
x) M core
+
+
xM mod
xM mod
Vsol
× 100 (2)
where M represents the mass of the surface-modified CeO2 NPs, Msol denotes the solvent mass, Mcore stands for the particle core mass, Mmod represents the mass of the modifier-attached particle, ρmod denotes the modifier density, ρmod signifies the core density, and Vsol expresses the solvent volume. The density of modifiers on the particle surface was
Fig. 3. TG-weight loss of surface modifiers on NPs under N2 atmosphere at a heating rate of 10 °C/min: (A) C8–CeO2, (B) C10–CeO2, and (C) C18–CeO2. 3
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Table 1 Modified state of the NPs (C8-CeO2, C10-CeO2, and C18-CeO2) used to prepare NFs based on TEM and TG-DTA analysis. NPs
C8-CeO2
C10-CeO2
C18-CeO2
Particle size (TEM) [nm] TGA weight loss fraction, x [-] Modifier coverage [(number of molecules) nm−2] Thickness of the modifier layer, T [nm] Density of free modifier molecules [g cm−3] Modifier density on particle surface, ρmod [g cm−3]
6.0 ± 1.0 0.12 3.9 0.87 0.910 1.08
7.0 ± 0.8 0.14 4.7 1.07 0.893 1.25
6.6 ± 1.8 0.21 4.5 1.90 0.847 1.12
200 s−1. Data obtained at higher shear rate conditions of 200–1200 s−1 were used for analysis.
(1.2 cm cone radius) depending on the NF amount. The cell temperature was maintained at 20 °C during all viscosity measurements. Each measurement point was obtained after 60 s of achieving constant shear rates on the samples. The measurements were repeated five times for each sample. Deviation of the measured viscosity at the same shear rate converged to less than ± 1.0% for all samples under the condition that the shear rate is higher than 200 s−1. Stable conditions with error in viscosity of less than 1.0% were achieved with a shear rate higher than
3. Results and discussion 3.1. NP surface properties The modifier coverage, which is defined as the number of bound
Fig. 4. UV–vis spectra of NFs composed of CeO2 NPs at different volume fractions: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/dodecane. (E) Volume fraction dependence of the absorbance at 800 nm wavelength. The linear relation between the absorbance (log10 (I0/I)) and log10Φ reflects the dispersed state. The sudden jump in the absorbance shows the initiation of the agglomeration of NPs. This change is used to identify NF with the maximum volume fraction retaining its dispersibility. 4
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modifiers per unit of surface area on the core particle surface, is an important factor affecting surface-modified NPs in terms of their dispersibility in solvents. At a higher modifier coverage, NPs can be hydrophobic [10,11]. The modifier coverage is calculable from the weight loss occurring during TG analysis and the size of the core particles as determined using TEM. Figs. 1(A)–(C) portray TEM images of CeO2 NPs with different modifiers. Figs. 2(A)–(C) show the particle size distributions obtained from TEM images. The results reveal that all the surface-modified CeO2 NPs have small core (CeO2) size of approximately 7 nm with a narrow monodispersed size distribution. Fig. 3 shows TG curves of the respective surface-modified NP samples. A gradual decrease in weight loss was observed at temperatures of 300–700 °C for all samples. Actually, the TG weight loss in this temperature range, which is higher than the boiling points of modifier molecules, indicates that the organic modifiers are not physically absorbed but are in fact chemically bonded to the NP surfaces [9]. The TG weight loss, which is attributed to the thermal decomposition of organic molecules in the products, reflects the number of surface modifiers on NP surfaces. The calculated modifier coverage on the CeO2 particles is quite high, as shown in Table 1. The maximum theoretical modifier coverage of surface modifiers on the metal oxide surface has been reported as 5.3 molecules nm−2 based on the cross-sectional area of an alkyl chain [36]. For comparison, the number of surface cerium atoms is 6.8 nm−2 at the (100) surface of CeO2. As might be readily apparent from Table 1, the calculated densities of modifiers are 19–40% higher than those in the original state at room temperature because of the high-packing structures of the modifiers and because of their alignment. These results, regarded in light of an earlier study [36], suggest that the modifiers are densely packed and nearly vertically oriented as quasicrystalline structures. This unique feature of surface modified NPs, where dense organic layers were formed on the NP surfaces, contributed to the high affinity of hybrid NPs to nonpolar solvents such as cyclohexane and the formulation of stable concentrated NFs. The volume fractions (Φ [vol.%]) of the CeO2 NFs were calculated based on the TEM and TG data. The values used for calculations are presented in Table 1. It is noteworthy that the estimated ρmod, the density of the organic modifiers bound to the surface of the cores, differs from the value found in their original states as free molecules, as explained above.
Table 2 Maximum volume fraction of transparent NFs found using UV–vis spectroscopy (shown in Fig. 3). Type of NF
Maximum Φ (vol.%) with transparency
C10-CeO2/cyclohexane C18-CeO2/cyclohexane C8-CeO2/decalin C10-CeO2/dodecane
23.3 0.2 1.0 0.1
absorbance is used as a criterion in this study to distinguish between transparent (dispersive) and opaque (agglomerative) NFs, as presented in Fig. 4(E). The limit of the volume fraction for obtaining transparent NFs was found using UV–vis spectroscopy (Fig. 4(E)). The determined values for each NF are presented in Table 2. Photographs of the four transparent NFs with the highest probable volume fraction and the volume fraction at which the NPs start to agglomerate are presented in Fig. 5. The NFs
3.2. NF dispersibility For this study, four types of CeO2 NFs with different modifiers in different solvents were prepared at various concentrations: C8–CeO2/ decalin, C10–CeO2/cyclohexane, C10–CeO2/dodecane, and C18–CeO2/ cyclohexane. Depending on the modifier–solvent affinity, the maximum volume fractions of NFs with completely dispersed particles differ with different combinations. When the NPs are dispersed completely, NPs exist as single particles in the solvent. Such NFs are transparent to visible light because the NPs are much smaller than the wavelength of visible light: Mie scattering does not occur. In fact, the NFs remain transparent until the NPs start to agglomerate to sizes comparable to visible light wavelengths. Agglomeration, i.e., the formation of secondary structures, was observed using UV–vis spectroscopy. Fig. 4(A)–(D) show the absorption spectra of the four NFs. Here, absorbance is defined as log10 (I0/I), where I0 and I respectively represent the intensities of the incident and transmission light. An increase in absorbance is observed with increase in the NP volume fraction of all NFs. Fig. 4(E) shows the volume fraction dependence of the absorbance at 800 nm for each NF, where Rayleigh scattering is expected and solvents have no absorption. The absorbance values at 800 nm increased with an increase in the volume fraction. However, no linear correlation with NP concentration, which is expected for complete dispersions, is observed for NFs in the high concentration range. The sharp increase in the absorbance suggests the agglomeration of NPs to structures with sizes on the order of hundreds of nanometers. The abrupt change in
Fig. 5. Photographs of NFs of four types with the highest concentration maintaining transparency (left column) and that of starting agglomeration (right column) evaluated using UV–vis spectroscopy: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/ dodecane. Numbers on the images show the volume fraction of each NF. 5
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Fig. 6. Viscosities of transparent NFs evaluated using UV–vis spectroscopy at different volume fractions as a function of the shear rate: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/dodecane.
Fig. 7. Viscosity of non-transparent NFs evaluated using UV–vis spectroscopy at different volume fractions as a function of the shear rate: (A) C10–CeO2/cyclohexane, (B) C18–CeO2/cyclohexane, (C) C8–CeO2/decalin, and (D) C10–CeO2/dodecane.
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classified via UV–vis analysis as complete dispersions also appear transparent in the images. The threshold volume fraction to obtain a transparent NF differs significantly for NFs of different types. For example, C10–CeO2/cyclohexane NFs remained transparent even at volume fractions as high as 23.3 vol.%. By contrast, C10–CeO2/dodecane NFs appeared agglomerated at 0.1 vol.%. The rheological characteristics of the NFs are analyzed in the following section based on dispersibility evaluated in this section. 3.3. Viscosity of dispersed NFs The viscosities of NFs with various volume fractions of NPs were measured by varying the shear rates. The NF viscosities are discussed based on the NF classifications presented in the previous section. Fig. 6 shows the rheological behaviors of dispersed NFs: most viscosities of the transparent NFs are low and independent of the shear rate, i.e., Newtonian fluids, irrespective of the modifier and solvent types. The only exception is the dispersed C10–CeO2/cyclohexane at 23.3 vol.%. Its viscosity increased with an increase in the shear rate, as shown in Fig. 6(A): it showed shear thickening behavior. That shear thickening behavior is visible irrespective of the dispersive behavior, as explained later. Except for the shear thickening cases, all the transparent or dispersive NFs are Newtonian fluids. 3.4. Viscosity of agglomerated NFs All the agglomerated NFs exhibited higher viscosities than those of the dispersed NFs. In contrast to the dispersed NFs, shear thinning behavior was observed in addition to Newtonian and shear thickening behavior in the case of agglomerated NFs. Shear thickening behavior was observed at high concentration ranges such as 29.4 vol.% for C10–CeO2/cyclohexane NF and 31.6 vol.% for C8–CeO2/decalin NF, as presented in Fig. 7(A) and (C). Shear thickening is observed in both dispersed and agglomerated NFs. However, the volume fraction range is limited to highly concentrated conditions: higher than approximately 23 vol.%. Results show that the origin of shear thickening is not the initial agglomeration but rather the high concentration. Some structures might form under shear at high concentrations irrespective of the initial dispersibility before shear applications. The NFs agglomerated at low concentrations such as 1.2 vol.% of C18–CeO2/cyclohexane and 0.2 vol.% of C10–CeO2/dodecane show Newtonian behavior, as presented in Fig. 7(B) and (D). An increase in the NP concentration caused clear shear thinning, as shown in Fig. 7(B)–(D), which is not observed in the case of the transparent NFs. The shear thinning behavior was observed only in the case of agglomerated NFs. Thereby, the origin of shear thinning can be attributed to agglomeration size of several hundred nanometers. Such agglomeration depends on the NP concentration and the affinity of NPs and solvents.
Fig. 8. Relative viscosity of NFs as a function of volume fraction of NPs: (A) Viscosity at the shear rate of 200 s−1, with plots unfilled showing dispersed NFs and plots filled showing agglomerated NFs. (B) After the application of shear force (the viscosity at the highest applied shear rates for each NF), with blue plots showing Newtonian, red plots showing shear thinning, and yellow plots showing shear thickening. For both (A) and (B), the solid line represents the Einstein model for low concentration; the dotted line shows the Happel model for high concentration. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
shear thickening), the relative viscosity at a shear rate of 200 s−1 is shown in Fig. 8(A). The relations between the relative viscosity and the volume fraction given by the Einstein viscosity equation for the low volume fraction suspension [40] and the Happel cell model [41] developed for highly concentrated fluids are presented in Fig. 8. The viscosity of each dispersed NF increased monotonically with the increase in the volume fraction, irrespective of the type of solvent. Then they are well-understood by these conventional models, as shown in Fig. 8. In contrast, the relative viscosity of the agglomerated NFs is scattered above the viscosities of the dispersed NFs. Even at equal concentrations, the viscosities of the agglomerated NFs are much higher than those of the dispersed NFs. The viscosity of some of the agglomerated NFs did not simply increase with an increase in the volume fraction of NPs, as shown in Fig. 8(A). The viscosities of the agglomerated NFs were apparently determined not only by their volume fractions. They were also affected by the degree of agglomeration. Fig. 8(B) portrays the volume fraction dependence of the relative viscosities at the highest applied shear rate for each NF. The final
3.5. Relation between viscosity and dispersibility The relative viscosities of the NFs (i.e., the ratios of the apparent viscosity of the NF to the viscosity of the solvent, r = NF / solv ) were calculated for comparison. The viscosities of solvents such as cyclohexane, decalin, and dodecane are independent of the shear rate: they are Newtonian fluids. The average viscosity values of cyclohexane (0.86 mPa·s), decalin (2.05 mPa·s), and dodecane (1.42 mPa·s) at 20 °C are consistent with the values reported earlier in the relevant literature [37–39]. Fig. 8(A) shows the relation between the relative viscosity and volume fraction of the NFs: unfilled symbols represent transparent NFs; filled symbols represent non-transparent NFs. The apparent viscosity of the Newtonian NFs was found from the slope of the shear rate vs. shear stress curve. These values were used to calculate the relative viscosity. For shear-dependent NFs (non-Newtonian; both shear thinning and 7
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apparent viscosity at the highest applied shear rate was used to calculate the relative viscosity for the shear-dependent non-Newtonian NFs. The symbols in Fig. 8(B) are blue for Newtonian fluids, red for shear thinning fluids, and yellow for shear thickening fluids. Under the application of shear stress to these agglomerated NFs, their viscosity decreased and approached the viscosity range of the transparent NFs, as shown in Fig. 8(b), suggesting that the deformation of agglomeration initially exists in non-transparent NFs. The initial agglomerated structure of NPs in these non-transparent NFs was possibly broken down by shear stress, similarly to behaviors found in studies reported earlier [25,26,42]. The viscosity of some of the agglomerated NFs remained higher than that of the dispersed NFs in Fig. 8(b), indicating that the NPs persistently agglomerated even under shearing force and indicating that the remnant agglomerates contributed to the increased viscosity of these NFs. At very high concentrations, NFs exhibit shear thickening irrespective of the initial dispersibility evaluated via UV–vis. Indeed, at concentrations greater than approx. 23 vol.%, C10–CeO2/cyclohexane (dispersed) and C8–CeO2/decalin (agglomerated) NFs showed shear thickening behavior, as denoted by yellow symbols in Fig. 8(B). Shear thickening was observed sometimes for concentrated NFs in which the NPs are self-organized under shear stress [43–45], probably because the average distance between the NPs is comparable to the size of NPs, i.e., the distance can be in the range of the potential curve between NPs [46,47].
[3] [4]
[5] [6]
[7] [8] [9] [10] [11]
[12]
4. Conclusions
[13]
Rheological behavior such as Newtonian behavior, shear thinning, and shear thickening was classified with dispersive behavior measured using UV–vis spectroscopy over widely various concentrations while controlling the affinity of NPs and solvents by changing organic modifiers. At lower concentrations (approximately less than 23 vol%), the relative viscosities of dispersive NFs show Newtonian behavior irrespective of the solvents or surface modifiers used. Shear thinning occurred only for non-dispersive NFs. After shear thinning, the viscosity approached the viscosity range of Newtonian NFs. Agglomeration of several hundred nanometers’ size and de-agglomeration by shear application are attributed to shear thinning. By contrast, shear thickening occurs in both dispersed and agglomerated NFs, but only in highly concentrated NFs of more than 23 vol.%. The origin of shear thickening is not the initial agglomeration but the structural formation of NPs under shear at high NP concentrations.
[14] [15] [16]
[17]
[18]
[19]
Declaration of Competing Interest [20]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[21]
Acknowledgments
[22]
This work was supported by JSPS KAKENHI Grants (Nos. JP 25249108, 16H06367), SIP Project, “Innovative design/manufacturing technologies on-demand on 3D additive manufacturing of structural functional materials and 3D devices through the creation of fluidic material”, the World Premier International Research Centre Initiative (WPI), and the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
[23] [24] [25]
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