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[Sadaki Samitsu](https://orcid.org/0000-0002-4139-1656), [Ryota Tamate](https://orcid.org/0000-0002-1704-1058), [Takeshi Ueki](https://orcid.org/0000-0001-9317-6280)

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[Effect of Liquid Properties on the Non-Newtonian Rheology of Concentrated Silica Suspensions: Discontinuous Shear Thickening, Shear Jamming, and Shock Absorbance](https://mdr.nims.go.jp/datasets/88d30fca-8c31-4387-8dc6-00467722a3be)

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Template for Electronic Submission to ACS JournalsEffect of liquid properties on the non-Newtonian rheology of concentrated silica suspensions: Discontinuous shear thickening, shear jamming, and shock absorbanceSadaki Samitsu,1* Ryota Tamate,1 Takeshi Ueki11National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanABSTRACT Concentrated particle suspensions exhibit rheological behavior, such as discontinuous shear thickening (DST) and dynamic shear jamming (SJ), which affect applications such as soft armors. Although the origin of these behavior in shear-activated particle–particle interactions has been identified, the effect of chemical factors, especially the role of liquids, on these behavior remains unexplored. Hydrogen bonding in suspensions has been proposed to be essential for frictional contacts between particles, and therefore, most studies on DST and SJ have focused on aqueous and protic organic media with a definite hydrogen bonding ability. To identify an alternative molecular mechanism, this study explored the effects of liquid polarity and aprotic nature on the rheological behavior of concentrated suspensions of silica microparticles. Owing to their excellent particle dispersion, the DST behavior of polar liquids was observed, independent of protic and aprotic liquids. In contrast, nonpolar liquids formed particle agglomerates because of the particle–particle attraction and became a paste at a high particle fraction. The SJ behavior was confirmed for three aprotic organic liquids (propylene carbonate, 1,3-dimethyl-2-imidazolidinone, and 1,3-dimethylpropyleneurea), suggesting hydrogen bonding ability of this aprotic liquids. The diverse mechanisms of shear-activated interactions between particles present material design possibilities for the non-Newtonian rheology of concentrated particle suspensions.Keywords:  Concentrated particle suspension, silica microparticle, non-Newtonian rheology, discontinuous shear thickening, dynamic shear jamming, hydrogen bond, aprotic liquidINTRODUCTIONSignificant changes in non-Newtonian rheological behavior strongly dependent on shear rate and shear stress are essential to realize optimal processing in the chemical, paint, and coating industries and develop mechanically responsive smart materials. This behavior is often observed in concentrated particle suspensions with particle fractions as high as 40–55 vol%.1–5 In steady-state shear flow, viscosity increases rapidly by one to two orders of magnitude above the critical shear rate; this behavior is referred to as discontinuous shear thickening (DST).6–13 The particle suspensions exhibit dynamic shear jamming (SJ) 14–17 and impact-activated solidification 17–19 when a high shear stress or impact force is applied, with the suspensions transiently responding similar to solids. The behavior are useful to realize the superior shock and bulletproof performances of soft armor.20–22In the field of physics, many studies employ experiments, numerical model analyses, and simulations to investigate the origin of the rheological properties.7,23–27 Although details remain controversial, it has gradually become common understanding that frictional interactions between particles affect both DST and SJ behavior.7,12,15 Other studies have discussed the effects of hydrodynamic forces on DST behavior. For example, Jamali et al.10 demonstrated DST behavior by simulating the Stokesian dynamics of the suspension of rough particles in the absence of frictional forces. Recently, Prabhu et al.28 experimentally demonstrated the DST of suspensions under the presence of only hydrodynamic forces. These different origins can help elucidate why some systems exhibit only DST behavior, while the others exhibit both DST and SJ behaviors.Despite the effect of the structural parameters of particles having been examined in several studies,8,16,29 a systematic investigation on chemical factors, such as the effect of liquid media, remains lacking. An aqueous suspension of cornstarch is commonly used as a model in physics research 23,30–32; however, it is not suitable for long-term usage because of the aging of cornstarch.33 Suspensions that can maintain their rheological properties over long periods are required for material applications. Chemically stable particles such as silica are suitable instead of cornstarch, and stable liquid media are required to replace the aqueous system. In contrast to the numerous studies reported for cornstarch suspensions in aqueous media, a limited number of DST and SJ behaviors were reported for non-aqueous suspensions using submicron colloids 6,11,22,29,34–39 and non-Brownian particles.40–42 For example, silica nanoparticles suspended in tetrahydrofurfuryl alcohol,6 ethylene glycol (EG), low-molecular-weight poly(ethylene glycol) (PEG), poly(propylene glycol) (PPG), 8,16,35,36,43 and ionic liquids;37 anisotropic calcium carbonate particles in PEG;29 latex suspended in EG and diethylene glycol;38 and colloidal particles of styrene-acrylonitrile copolymers suspended in EG22 have been reported thus far. Most of these studies used protic liquids, such as aqueous solutions, glycol-based liquids, and low-molecular-weight PEG and PPG. In terms of DST behavior, there are a few experimental results besides those of the protic liquid suspension, poly(vinyl chloride) particles suspended in dioctyl phthalate,13 and glass particles in mineral or silicone oil.15,23,44 To the best of our knowledge, SJ behavior is yet to be demonstrated in aprotic liquids. Hydrogen bonding has received considerable research attention because it plays an important role in particle–particle frictional interaction. For example, Raghavan et al. introduced a solvation layer around silica to address the stabilization of colloidal silica suspensions.34 Swarna et al. addressed the role of hydrogen bond interactions in the DST of aqueous cornstarch suspensions.45 James et al. demonstrated that only protic liquids exhibit SJ behavior, and pure dimethylformamide (DMF), an aprotic liquid, did not show SJ behavior.15 They proposed hydrogen bonding as the origin of frictional particle–particle contact for SJ behavior.15 Other results suggesting an origin of particle–particle frictional interaction besides hydrogen bonding have been reported. Oyarte Gálvez et al. demonstrated that concentrated cornstarch suspensions exhibit DST and SJ in aqueous media; however, not in ethanol.46,47 Comtet et al. directly measured the particle–particle interaction of cornstarch in water and plasticized poly(vinyl chloride) particle in mineral oil, and investigated the relationship of the interactions with DST behavior.47 These studies addressed the particle swelling or steric repulsion of solvated polymers as another mechanism of frictional particle–particle interaction for DST and SJ behavior.46,47 The importance of shear-activated interactions between particles is common to DST and SJ behavior; however, the origins may be diverse. As examples of the various origins of particle–particle interactions, Bourrianne et al. suggested solid friction and hydrodynamic forces as physical factors and hydrogen bonding and particle swelling as chemical factors.43In this study, the concentrated suspensions of micrometer-sized silica particles were prepared using 14 liquid media to explore the molecular mechanism of shear-activated particle–particle interaction between non-swelling particles. The rheological properties were investigated using steady-state shear flow, pull-out test, and ball-drop test for DST, SJ, and shock absorbance, respectively. Protic and aprotic organic liquids were examined by selecting the polarity of the liquid systematically. The DST behavior was observed for both protic and aprotic polar liquids and attributed to the good dispersion of silica particles in the polar liquids. In contrast, nonpolar liquids formed particle agglomerates because of considerable particle–particle attraction and became a paste at a high particle fraction. To the best of our knowledge, this is the first study to confirm the SJ behavior was confirmed for three aprotic liquids. Protic liquids can be either hydrogen bond donors or hydrogen bond acceptors because they have dissociable hydrogen atoms bound to electronegative atoms. Only protic liquids form hydrogen bonds because of the complementary behavior. However, hydrogen bonding properties are not inherently limited to protic liquids alone. Our results suggest that DST and SJ behaviors in concentrated particle suspensions can be extended to aprotic liquid systems.The remainder of this paper is organized as follows: First, we introduce the rheological behavior of concentrated silica suspensions of propylene carbonate (PC) and 1,3-dimethyl-2-imidazolidinone (DMI), which are representative examples. Next, we present the rheological behavior of other organic liquids, followed by an evaluation of the dispersibility of the silica particles in terms of the relative permittivity of the liquids. Further, we demonstrate the effects of particle size, size distribution, and porous structure of silica particles. Finally, we discuss the relationship between the polarity and hydrogen bonding ability of the liquids, particle dispersion, and rheological behavior.EXPERIMENTAL SECTIONSilica microparticles and organic liquids were purchased from the chemical companies listed in Tables 1 and S1, respectively. The abbreviations and their properties are summarized in Tables 1 and 2. Silica particles were used as received because of their low moisture absorption of <0.1%.Table 1. Information about silica particles. ID Supplier† Grade D (μm)‡ Porosity Polydispersity SP1 NS KE-S250 2.5 Nonporous Monodisperse SP2 AGC NP-100 10 Nonporous Polydisperse SP3 SP1, the surface of which was chemically modified with octadecyl chains. Nonporous Monodisperse SP4 AGC H-121 12 Porous Polydisperse SP5 AGC H-121-ET 12 Porous Polydisperse SP6 NS KE-S50 0.5 Nonporous Monodisperse†NS: SEAHOSTARTM; Nippon Shokubai Co., Ltd. AGC: SUNSPERA, AGC Si-Tech Co., Ltd. ‡The particle diameters were obtained from the catalog information provided by each supplier.Table 2. Properties of organic liquids.  Liquid Abbreviation Polarity Protic nature εr ηL(mPa s) Propylene carbonate PC H – 64.9 2.5 γ-butyrolactone gBL H – 39.0 1.7 Ethylene glycol EG H + 37.7 15.4 1,3-dimethyl-2-imidazolidinone DMI H – 37.6† 1.9† 1,3-dimethylpropyleneurea DMPU H – 36.12 48 2.9 48 N-methylpyrrolidone NMP H – 32.2 1.7 Benzyl alcohol BnOH M + 12.7 6.5 Triethyl phosphate TEP M – 10.8 2.1 2-phenylethyl alcohol PEA M + 10.75(30 ℃) 49 11.4 49 Tributyl phosphate TBP M – 8.9 3.4 Tetraethylene glycol dimethyl ether G4 M – 7.79‡ 3.3‡ Dibenzyl ether DBE L – 3.9 3.9 Silicone oil (KF-96L-2cs) S-oil L – 2.42†  1.7†  n-hexadecane HD L – 2.1 2.8†The values were obtained from product datasheets provided by suppliers. ‡The values were obtained from the Springer Materials database. Polarity: H, polar solvent with εr > 11; M, medium polar solvent with 11> εr > 5; L, nonpolar solvent with εr < 5; and protic nature: + and –, solvent with and without proton exchange abilities, respectively.Concentrated silica suspensions were prepared by mixing silica particles with an organic liquid based on the procedure reported in a previous study.50 Suspension samples are denoted by connecting an organic liquid used as liquid medium, particle fraction ϕ of the unit of percentage volume (vol%), and particle ID. In suspension SP1, the particle ID was not specified. PC-565-SP1 or PC-565 represent the silica suspension prepared by mixing silica particle SP1 with liquid medium PC at a ϕ of 56.5 vol%. SP1 was used as the representative particle in the suspension samples. The rheological behavior of concentrated silica suspensions were characterized using steady-state shear flow, pull-out tests, and ball-drop tests. Details on these characterizations are reported elsewhere.50 PC and DMI were selected as representative liquid media for rheological characterization. Their suspensions were prepared using SP1 at ϕ of 40.0–59.0% and measured using steady-state shear tests. A suspension placed in the measurement geometry was visually checked for the absence of air bubbles. The apparent shear viscosity η was evaluated by dividing the shear stress σ by the shear rate γ (η = σ / γ).4 Shear thickening behavior provides a power law scaling of σ versus γ with the exponent of α > 1 (σ = γα). The viscosity η was plotted on both logarithmic axes against shear stress σ or shear rate γ. η is expressed by the power law of σ using the exponent of αs (η = σαs, where αs = 1 – 1/α), and αs was determined by the slope of a linear fit of log η as a function of log σ in the shear thickening regime. The SJ behavior of PC suspensions was evaluated by a pull-out test at various ϕ. A cylindrical rod embedded in the suspension was pulled out perpendicular to the suspension surface, and the transient force during the pullout was recorded versus the rod displacement. The force was almost zero because of the insufficient pull-out speed of 8 mm/s or slower when the test was performed with a high-performance rheometer (Anton Paar MCR102, Austria).15,50 High-speed pull-out tests were performed using a home-built apparatus equipped with a force gauge (ZTA-100N, IMADA, Japan) and a linear actuator (US6T, THK, Japan) at a pull-out speed of 0–360 mm/s. The suspension was filled in a cylindrical glass vial (inner diameter = 13.6 mm; height = 30 mm). An aluminum rod (diameter = 6 mm) was inserted into the suspension at a depth of 5 mm and pulled out after 1 min equilibrium. Scheme 1 presents the suspension preparation and rheological characterization.Scheme 1. Schematic illustration of this study. Concentrated suspensions of micrometer-sized silica particles were suspended in 14 types of organic liquids with ϕ of 40–60%. The rheological properties of the suspensions were characterized using steady-state shear flow to determine the shear thickening behavior (continuous shear thickening (CST) or DST). The dynamic SJ behavior was determined using a pull-out test, and the shock-absorbing property was measured using a ball-drop test.The size of silica particles was observed directly using a scanning electron microscope (SEM; Miniscope TM3000, Hitachi Co., Japan, or S-4800, Hitachi High-Tech Corp., Japan). The size distributions of silica particles and their aggregates were measured using a laser diffraction particle size analyzer (SALD-2100, Shimadzu, Japan). A small number of silica particles was suspended in the liquid and ultrasonicated for 15 min, followed by diluting the mixture with the same liquid to adjust the scattered light intensity to the appropriate value. The size distribution was calculated assuming a spherical shape. The complex refractive index of silica particles, N = n + i κ, was used to consider light attenuation as the imaginary part of the complex refractive index; N = 1.45−0.5i. The averaged diameter and particle size at the 75th volume percentile, Dav and D75, respectively, were determined by the laser diffraction analysis of dilute silica suspensions in methanol. Oscillatory shear measurements were performed using a MCR 102 rheometer equipped with a parallel-plate geometry (diameter = 25 mm) to evaluate gelation behavior of suspensions. The geometric gap was set to 1 mm. The gap was optimized to be smaller than 1 mm for suspensions with low viscosity and poor retention on a 1-mm gap. The frequency dependence was measured at 20 °C at an amplitude of 1% and a frequency range of 0.1–100 rad s−1. RESULTSPreliminary screening of dense starch suspension in organic liquidsLiquids used with concentrated suspensions must adhere to the following criteria: (i) liquid state at room temperature, (ii) high boiling point to inhibit evaporation during characterization, and (iii) low viscosity to ensure flow even when large amounts of particles are mixed. A liquid that is easy to handle in experiments and has little odor, low toxicity, and low corrosiveness is desirable. The 14 liquids with widely different relative permittivity values that were selected based on the three criteria in the handbook 51 and our expertise, i.e., (1) melting point below 20 °C, (2) boiling point above 200 °C, and (3) viscosity below 20 mPas, are summarized in Table 2.Preparation of concentrated silica suspension in organic liquidsSilica particles exhibit excellent shape stability in organic liquids and are commercially available in a variety of sizes, polydispersities, and porosities, making them suitable as model particles for concentrated suspensions in organic liquids. Therefore, concentrated silica suspensions were prepared in organic liquids to avoid uncertain factors. Nonporous, monodisperse spherical silica microparticles with a diameter of 2.3 μm, SP1 (Figure 1a), were suspended in the 14 organic liquids listed in Table 2. The liquids were stirred by hand as a preliminary screening experiment to test the rheological behavior at a wide ϕ range. In nonpolar liquids such as n-hexadecane (HD) and silicone oil (S-oil), the particles flow easily at low ϕ; however, they become a viscous paste for ϕ as high as 35% (Figure 1b). Within these ϕ ranges, characteristic rheological behavior that depend significantly on the shear rate, such as DST and SJ, which were not detected. In highly polar liquids such as PC and DMI, the suspensions were fluid even at high ϕ above 50 % (Figures 1c and 1d). At high ϕ, below which the suspensions became powdery, the suspensions exhibited characteristic rheological behavior similar to that of the aqueous cornstarch suspensions. There is a significant difference in the rheological behavior of concentrated silica suspensions for nonpolar and highly polar liquids. The rheological behavior was characterized quantitatively using steady-state shear flow, a high-speed pull-out test, and a ball-drop test. Figure 1. (a) Scanning electron micrograph of silica particle SP1. (b-d) Photographs of concentrated silica suspensions: (b) HD-400, (c) PC-565, and (d) PC-590. The movies of the result can be supplied as Supplementary Videos S1-S3.Steady-state shear flowAt a low ϕ of 40.0–45.0%, the PC suspensions showed a CST behavior wherein η increased slowly with σ. Further, η increased with σ steeply when ϕ increased to 53.0–58.4% (Figure 2). Brown et al. proposed a simple criterion to separate DST from CST using the slope value αs in the shear thickening regime of a log η–log σ plot.4 Bourrianne et al.43 recently proposed a sophisticated procedure to determine σ-dependent CST and DST behavior. They calculated the σ dependence of αs by differentiating log η by log σ and plotted αs against ϕ and σ to obtain a state diagram of CST and DST behavior. The ideal behavior of DST suggests that viscosity is expected to change discontinuously at a given shear rate, corresponding to αs = 1 on log η–log σ plot. However, ideal discontinuity is not observed for some samples because of some experimental limitations. Therefore, for the sake of simplicity, this study used Brown’s criterion.4 The maximum value of the slope of the η–σ plot at a high σ region, αs < 0.5 and ≥ 0.5 correspond to CST and DST behavior, respectively (upper panel of Figure 5). The minimum value in the η–σ plot, ηmin, increased with an increase in ϕ. The suspensions lose flowability when ϕ increases over 59%. The steady-state shear flow behavior cannot be measured because of the very high η required for operating the rheometer properly. Further, the DST behavior of PC suspensions was confirmed by the jump of η at a critical γ in the η–γ plots (Figure S1). The DMI suspensions showed an η–σ plot qualitatively similar to that of PC suspensions, where the DST behavior was confirmed at ϕ of 50.0–59.0%.Figure 2. Steady-state shear test. Apparent viscosity η is plotted as a function of shear stress σ: (a) PC suspensions and (b) DMI suspensions.High-speed pull-out testWhen the pull-out tests were performed at a pull-out speed of 100 mm/s or higher, PC-565 exhibited a finite force to resist the pull out. The maximum force Fmax was 7.4 N at a pull-out speed of 100 mm/s; Fmax increased up to 12.2 N as the speed increased to 360 mm/s (Figure 3a). James et al. performed pull-out tests for determining SJ behavior for the concentrated suspensions of cornstarch and polymer particle in aqueous glycerol 15. They demonstrated that the force generation above the critical value of the pull-out speed is a characteristic of the SJ suspension that changes from fluid- to solid-like behavior under high shear deformation17. The force returns to zero when the rod is sufficiently pulled up. This can be attributed to the rupture of the sample, which is consistent with the solid-like behavior of the SJ suspension. When varying the ϕ of the PC suspensions, all those with ϕ ≥ 56.5% showed SJ behavior with a large Fmax above the critical speed. The critical speeds generating a finite Fmax decreased with increasing ϕ, varying from 10–100 mm/s at ϕ ranging from 56.5–59.0% (Figure 3c). The maximum height at which a finite pull-out force appeared was independent on the pull-out speed (Figure 3a); however, it increased with increasing ϕ (Figure 3b). The result suggests that the deformation behavior of the SJ state governed by particle–particle frictional contact depends strongly on ϕ and weakly on the shear rate. Pulling tests were performed by systematically varying ϕ and pull-out speeds. The SJ behavior diagram was plotted against ϕ and pull-out speed (Figure 3d). The SJ behavior was confirmed at high ϕ and high pull-out speed, i.e., the high shear rate in the diagram, which is qualitatively consistent with that reported in the previous studies.Figure 3. Transient forces were plotted as a function of rod displacement on pull-out tests for (a) PC-565 at different pull-out speeds and (b) PC suspensions at the pull-out speed of 360 mm/s. (c) Pull-out speed versus the Fmax was determined via the pull-out tests. (d) The diagram of SJ behavior for the PC suspensions was plotted as functions of ϕ and the pull-out speed. The fluidic and SJ behavior of the suspensions are indicated by blue circles and red squares, respectively.Ball-drop testThe shock-absorbing property of PC suspensions was evaluated using a ball-drop test. Peters et al. investigated a rigid sphere in free fall on a concentrated suspension of cornstarch in aqueous glycerol and tracked the trajectory of the sphere.14 In this study, the transient forces in the vertical direction were recorded during the strike (Figure 4). In the ball-drop test, PC-500 that showed no DST behavior presented a large peak force fpeak exceeding 90 N within 0.5 ms after the strike. The force plot showed a second fpeak at 65 ms as the steel ball bounced once from the bottom of the sample container and fell back into the suspension, indicating minimal shock absorption.14 In contrast, PC-550 with a DST behavior exhibited a very small fpeak of less than 12 N and no vibrations, thereby indicating sufficient shock-absorbing properties. When the ϕ increased further to 59.0 %, PC-590 showed a higher fpeak than that of PC-550.Figure 4. Transient force recorded on ball-drop tests of (a) PC-550, (b) PC-550, and (c) PC-590. Subsequent ball-drop tests were performed for PC suspensions at ϕ of 50.0–59.0%, and the fpeak values were plotted versus ϕ (Figure 5c). The fpeak values were high and no shock-absorbing property was presented for ϕ lower than 50 vol%, where the DST behavior did not appear in the shear tests. The fpeak decreased rapidly as ϕ exceeded 50%, where the DST behavior emerged. The fpeak reached a minimum value of 12 N at a ϕ of 55.0–55.5% and increased to a constant value of ~50 N with an increase in ϕ. PC-550 had the highest shock-absorbing property, yielding a 13 % fpeak compared with that of PC-500.The shock-absorbing property was very sensitive to ϕ and showed a minimum at the ϕ in the range where DST behavior appeared and where SJ behavior started (Figure 5). This behavior is qualitatively consistent with the results of a previous study on the concentrated suspensions of starch particles.50 The difference in the absolute values can be attributed to the effect of material factors, such as the average particle size, particle size distribution, particle shape, viscosity of the liquid medium, and surface chemistry of the particles. In addition, the depth of suspension affects the quantitative behavior of the ball-drop test.52 In the DST region, the shock absorbing property increases with increasing ϕ. However, the suspension behaves as a solid once the SJ behavior appears, and its elastic behavior partly reduces the shock-absorbing property. Two different mechanisms affect the shock absorption properties of the suspension in the low and high ϕ regions, resulting in the development of shock absorption behavior only in a narrow ϕ range.Figure 5. ϕ dependence on (a) the slope of the η–σ plot in a steady-state shear flow test, (b) Fmax of the pull-out test, and (c) fpeak on the ball-drop test for PC suspensions, as characterized in Figures 2, 3, and 4.Naald et al. investigated the impact properties of concentrated fumed silica suspensions in EG and PEG using a rod impactor.36 A large deformation velocity occurred locally and only around the impactor for the EG suspension that exhibited only the CST behavior. In contrast, for the PEG suspension that exhibited DST behavior, the sample deformed widely and uniformly like a solid, resulting in low velocity and good impact mitigation. Although the previous study used fumed silica particles, which is a submicrometer irregularly shaped aggregate of colloidal silica proposed for the rod impactor, the momentum during the ball strike instantly propagated widely around the ball, reducing the local impact force and significantly improving impact mitigation compared to that for a viscous fluid.Effect of liquid properties on concentrated silica suspensions examined by steady-state shear flowThe steady-state shear flow was measured for concentrated SP1 suspensions in organic liquids and aqueous suspensions for quantitatively evaluating the effect of liquid media (Figure 6). The ϕ was fixed at 56.5%, where the DST behavior was obtained for both PC and DMI. Depending on the εr of liquids, the suspensions exhibited three types of η–σ plots. Polar liquids such as gBL exhibited an αs of the η–σ plot close to 1, indicating DST behavior. Medium εr liquids such as TBP showed only a small increase in η and αs < 0.5, suggesting CST behavior. Less polar liquids such as G4 afforded considerably high, σ-independent η, which was similar to that of a paste. Nonpolar S-oil and HD mostly lost the flowability of the suspensions and could not be measured by steady-state shear flow.Figure 6. Steady-state shear tests of SP1 suspensions shown in the η–σ plot. The suspensions showing (a) DST behavior (square symbols), (b) suspensions presenting CST (circle symbols) or paste-like behavior (triangle symbols).Steady-state shear tests provided characteristic rheological parameters such as ηmin and αs, where ηmin represents the flowability of concentrated suspensions in the low σ range, and αs characterizes the increase in η in the high σ range. The double logarithmic plot of ηmin versus the viscosity of liquid media ηL confirmed a positive correlation between DST and CST behavior (Figure 7a). When the αs of the 15 suspensions were plotted versus the εr of liquids, they are classified into three groups: CST, DST, and paste (Figure 7b). The CST and DST were assigned based on whether the αs value was smaller or larger than 0.5, respectively. The pastes were identified by stirring them manually with a hand as it was impossible to measure them using a steady-state shear flow test. The data points of DST behavior and pastes were located at high and low εr ranges, respectively. The εr range of 5–15 is the boundary region, where suspensions exhibiting DST, CST, and paste-like behavior appear. According to the correlation shown in Figure 7b, the εr of liquid media was visualized quantitatively as the decisive factor not only in the presence or absence of DST behavior, but also the αs values of suspensions.42Figure 7. Steady-state shear flow tests for SP1 suspensions at the ϕ of 56.5% (red: DST, blue: CST, purple: paste). (a) ηmin in suspension versus the viscosity of liquid media, ηL, was plotted in double logarithmic scales. (b) αs value in the η–σ plot versus the εr of liquid media. The ηmin and αs were plotted for SP1 suspensions prepared by varying the ϕ and types of liquid medium (Figure 8). As demonstrated for the concentrated suspensions of cornstarch in water 53 and polymer particle in density-matching organic solvent mixture,9 ηmin, which is almost similar with the viscosity of the onset of DST, rapidly increases when ϕ approaches a critical ϕ value smaller than that of the densest amorphous packing for the frictionless hard sphere ϕRCP of 0.64. Further, Brown et al. reported that αs increases with ϕ and approaches 1, 4,32 high αs rarely appears in the low ηmin range, and this trade-off relationship is confirmed in the experiment. Material engineering for selecting particles and liquids is necessary to obtain concentrated suspensions that show a rapid η increase on DST and simultaneously flow easily at a low shear stress. Baumgarten and Kamrin 54 formulated a general constitutive model for concentrated particle suspensions that connect the mathematical model and material design of particle suspensions using the parameters of the critical volume fraction for shear jamming, critical state volume fraction associating Reynolds’ dilation, and fraction of frictional contacts between particles. The suspensions using PC and DMI as liquid media displayed many data points located near the upper bound of the tradeoff, confirming excellent DST behavior. Figure 8. αs was plotted as a function of ηmin for 26 suspensions of SP1 using different organic liquids and varying ϕ. Suspension samples are denoted by liquid and ϕ; for example, PC-565 represent the suspension in PC at a ϕ of 56.5 vol%.Effect of liquid properties examined by high-speed pull-out testTen organic liquids that exhibited DST or CST behavior in steady-state shear tests were selected and the SP1 suspension at a ϕ of 56.5% were examined by pull-out tests to evaluate their SJ behavior. The Fmax values were plotted against the pull-out speeds for each liquid (Figure 9). The DMPU suspension exhibited the largest Fmax of 18.7 N at 360 mm/s and the lowest pull-out speed of 50 mm/s for the SJ behavior, indicating pronounced SJ behavior. The Fmax increased monotonically with the pull-out speed. Further, PC and DMI exhibited obvious SJ behavior as the speed increased to 100 and 250 mm/s, respectively. PEA with εr = 10.75 showed the CST behavior and presented a moderate Fmax at a speed faster than 200 mm/s in the high-speed pull-out test, indicating moderate SJ behavior. gBL and NMP, which have high εr values and exhibited DST behavior, showed no force peaks even at a pull-out speed of 360 mm/s. BnOH and TBP, which showed CST behavior, exhibited a small Fmax of ~5 N in the high-speed region. The DST behavior in the steady-state shear test well correlated with the range of εr; however, the Fmax in the pull test did not correlate completely with εr either. Figure 9. High-speed pull-out tests for SP1 suspensions in ten organic liquids. The ϕ of the suspensions was fixed to 56.5%. (a) Fmax were plotted as a function of pull-out speeds. (b) Maximum Fmaxs for SP1 suspensions in various liquids, which were measured at the pull-out speed of 300 mm/s. Colored bars represents the SJ behavior of a suspension: (red) strong, (orange) medium, and (yellow) weak SJ.Effect of liquid properties examined by ball-drop testBased on the results of the steady-state shear flow and high-speed pull-out tests, two organic liquids that exhibited different rheological behavior in silica suspensions were selected to compare their shock-absorbing properties using ball-drop tests. DMI exhibited DST and SJ behaviors, whereas TEP only exhibited CST behavior and behaved as a fluid over the entire parameter range in our pull-out tests. The suspension exhibited a small fpeak of less than 11 N in the transient force curve when the ball struck DMI-545, and no vibrations occurred. TEP-565 exhibited a moderate fpeak of 30 N, and the sample stage vibrated up and down. DMI and TEP suspensions under varying ϕ of 50.0–59.0% were evaluated by ball-drop tests, and the fpeak were plotted versus ϕ (Figure 10b). DMI-545 exhibited good shock-absorbing properties similar to those of PC-550. The DMI suspensions exhibiting a fpeak smaller than 30 N were obtained in the ϕ range of 53.5–55.5%, which was considerably wider than the ϕ range of 55.0–55.5% for the PC suspensions. For TEP, the fpeak decreased gradually with an increasing ϕ; however, it reached only 30 N at a high ϕ of 56.5%. This comparison confirms that DMI exhibits excellent shock absorption, whereas TEP has less shock absorption, suggesting that the SJ behavior provides good shock-absorbing properties.Figure 10. (a) Transient force recorded on ball-drop tests of DMI-545 (left) and TEP-565 (right). (b) ϕ dependence on the fpeak recorded on the ball-drop tests for DMI (left) and TEP suspensions (right).Dispersion stability of micrometer-sized silica particles in organic liquidsThe dispersion stability of SP1 in liquids was characterized by visual inspection and particle size analysis to elucidate the relationship between the εr of liquids and rheological behavior of SP1 suspensions. The effect of interparticle interactions on the agglomeration of colloidal silica particles were evaluated by sedimentation experiment.55,56 At a low ϕ of 1%, SP1 dispersed well over several tens of minutes in polar PC and EG; however, it sedimented in a few minutes in nonpolar S-oil and HD (Figure 11a). In PC and EG, the particle showed sharp size distributions with average size Dav of 2.0 and 1.9 μm, respectively. The Dav were consistent with the average particle diameter imaged with SEM (Figure 1) and confirmed a good dispersion of SP1. S-oil and HD presented large agglomerates of SP1 with the Dav of 5.7 and 26.4 μm, respectively (Figure 11b). The result indicates that SP1 particles spontaneously agglomerate in the liquids with εr < 4 (Figure 11c) because of the strong particle–particle attraction, which is consistent with the sedimentation observed visually. Sedimentation behavior of silica particles has been reported in nonpolar liquids such as cyclohexane,56 mineral oil,57 and decalin, tetradecane and hexadecane.58Figure 11. Dispersion stability of SP1 suspensions in organic liquids. (a) Photographs of SP1 suspensions with the ϕ of 1% were taken 15 min after ultrasonication. SP1 dispersed well in PC and EG, while sedimented in HD and S-oil. (b) Size distributions and (c) average sizes of SP1 agglomerates in each liquid.At a high ϕ of 35%, although polar PC-350 and EG-350 maintained high fluidity, nonpolar S-oil-350 and HD-350 became soft pastes that easily deformed when touched with a spatula; however, they did not flow even when tilted (Figure 12). To elucidate dispersion of SP1, the suspensions were analyzed quantitatively by the frequency dependencies of the dynamic storage modulus G′ and loss modulus G″ (Figure 12). PC-350 and EG-350 suspensions presented the G″ of 0.8 Pa at 10 rad/s and monotonically increased with increasing ω. The G″ was more than four orders of magnitude larger than G′, confirming viscous liquid-like behavior. In contrast, S-oil-350 and HD-350 achieved G″ similar to G′ and was almost independent of frequency, showing typical paste- or gel-like behavior. Previous studies also reported the similar gel-like behavior for fumed silica suspension in mineral oil 57 and in 1-heptanol, EG dimethyl ether, propylene glycol dimethyl ether, PEG dimethyl ether,34 in PEG11 and PPG.43 The G″ was 2000 Pa at 10 rad/s, which is three orders of magnitude larger than those of PC and EG. The results of the dynamic mechanical analysis were consistent with those obtained via visual inspection and manual stirring tests. The nonpolar liquid did not spread uniformly between the polar silica particles when ϕ ≥40 %, leading to a loose network of heterogeneous particle agglomerates containing many voids.59 The particle network generated a certain yield stress against shear deformation. The yield stress causes loss of typical DST because DST behavior requires good fluidity in the low σ range.30Figure 12. Rheology of SP1 suspensions at ϕ of 35.0%. Photographs of inverted vials and frequency dependence of dynamic storage modulus (G′: closed) and loss modulus (G″: open). Fluidic behavior (left) and paste-like behavior of suspensions (right) were obtained for polar and nonpolar liquids, respectively.Effect of the structural parameters of silica particlesSilica particles with different characteristics such as particle size, particle size distribution, surface functional groups, and porous structure were examined to verify the presence or absence of DST behavior (Figure 13). PC was used as the liquid medium because of the excellent DST behavior for SP1. The scanning electron micrographs of the particles are shown in Figure 13(a). The presence or absence of particle size polydispersity and porous structures are listed in Figure 13(c). The ϕ was optimized via manual sensing tests for each particle because the rheological behavior of concentrated particle suspensions is very sensitive to ϕ 32. The optimal ϕ depends slightly on particle size and size distribution for non-porous spherical particles, and it depends considerably on porosity for porous particles. Although most particle suspensions require a high particle fraction of 40–55% to exhibit DST,1–5 porous particles SP4 and SP5 exhibit DST behavior at a low ϕ of 22.0-25.0% Such a low φ for DST behavior was found in fumed silica suspended in PEG and glycerol, which had a DST behavior with ϕ around 10%.39,43 Fumed silica has a hierarchical structure, and its secondary particles are composed of a fractal structure of primary particle aggregates that have many small voids and absorb liquid in the voids. Similarly, porous particles absorb most of the liquid in their pores, and therefore, the amount of liquid lubricating between particles is considerably less than the total amount of liquid. Thus, suspensions of porous particle exhibit DST behavior at a lower particle fraction than the suspensions of nonporous particles. Anisotropic particles also exhibit DST behavior at lower particle fractions;16 however, this can be attributed to anisotropic particles having geometric effects that inhibit tangential sliding and rotational motion. In this study, SP6 particles with the smallest diameter showed strong shear thinning in the low shear stress region and DST behavior with large onset stress. Previous studies reported that for particle sizes where the effect of gravity is negligible, the onset stress of DST increases with a decrease in particle size,4,8,9 which is consistent with the SP6 results. The smaller the particle size, the greater is the particle–particle interaction, resulting in silica particles being more likely to agglomerate.8 The shear thinning behavior appears in the low shear stress range because a weakly aggregated structure is destroyed by shear. The results confirmed that ϕ should be finely optimized for particles used to gain DST behavior. The amount of liquid required for a suspension to exhibit DST behavior is strongly correlated with the volume of voids inside the particle packing, and it is strongly affected by the shape, anisotropy, and porosity of particles, and less so by the particle size and size distribution. In other words, porous silica particles can present DST behavior once ϕ is optimized. The αs of SP3, where the particle surface is treated with alkyl chains, decreased slightly from that of SP1. Further, for porous particles, SP5, whose particle surface was coated with silicone, showed a reduced αs compared to untreated SP4. These results indicate surface treatment with alkyl chains or silicone reducing the particle–particle friction of silica particles. Owing to the suitable selection of liquid medium and the optimization of ϕ, DST behavior was confirmed for various silica particles including small and large spheres, porous and polydisperse particles, and surface chemistry of silica.Figure 13. (a) SEM images of silica particles. (b) η–σ plots measured by the stead-state shear flow tests for silica suspensions in PC using various types of silica particles. The ϕ was finely optimized for each particle. (c) Plot of αs (left axis) and ηmin (right axis) for silica suspensions shown in the panel (b). The information of the particles was tabulated on the bottom part of the plot.DISCUSSIONThe results of dispersion stability (Figures 11 and 12), steady-state shear flow (Figures 6 and 7), and high-speed pull-out tests (Figure 9) of SP1 suspensions are summarized in Table 3. SP1 particles produce large agglomerates in organic liquid with εr < 5 because of considerable particle–particle attraction. At a higher ϕ, the agglomeration forms loose networks, leading to a paste showing a certain yield stress. Thus, they lose fluidity and do not exhibit DST behavior. Polar liquids stabilized the dispersion of SP1 particles and inhibited their agglomeration. Further, they wet the silica particles uniformly and spread them into the narrow gaps of the densely packed silica particles. Such good wettability creates hydrodynamic lubrication between concentrated particles and results in high flowability in the low σ range. Concentrated SP1 suspensions forming a stable sol state exhibit DST behavior when a sufficiently high σ is applied. The DST behavior was observed for six liquids with εr >15, independent of whether they are protic. The DST behavior was governed by the dispersion stability of SP1 particles, and thus, the polarity of the liquid. Table 3. Results of the dispersion characterization and rheological properties of the suspension based on the εr and protic nature of liquidsStability of dispersion: +; single particle: −; and particle agglomerates. SJ behavior: strong, Fmax ≥ 10 N; medium, 10 > Fmax ≥ 5 N; and weak, Fmax < 5 N; and no, no peak detected. Paste-like samples were not measured by the pull-out test. The empty columns indicate conditions that were not measured experimentally.We comprehensively investigated the effect of 14 organic liquids, and found strong SJ behavior for DMPU, DMI, and PC, which are aprotic liquids with C=O bonds, and medium and weak SJ for protic liquid such as EG, BnOH, and PEA (Figure 9 and Table 3). Meanwhile, the SJ behavior was not observed in gBL and NMP, which have C=O bonding similar with the former three liquids. The former three aprotic liquids exhibiting strong SJ behavior not only have largely polarized C=O bond but also have considerable symmetry on the molecular structure, which can affect the hydrogen bonding ability of the liquids. The hydrogen bond-forming ability depends on electron charge transfer,60 which depends on both the type of chemical bond and molecular geometry, resulting in a complicated result. For example, Delavoux et al. measured the liquid structures of PC and 1,2-glycerol carbonate by isotope substitution neutron scattering and reported that aprotic PC is hydrogen-bondable, whereas protic 1,2-glycerol carbonate is not.61 This result is counterintuitive given the simplistic criteria for the hydrogen-bonding capacity of protic liquids. If DMPU, DMI, and PC have hydrogen bonding ability, then this is consistent with James et al. ’s assertion that a liquid with hydrogen bonding ability can produce SJ behavior.15 The suspensions in gBL and NMP exhibited DST and no SJ behavior. This suggests the possibility that origins of DST and SJ behavior are not necessarily the same and has been indicated by Jamali et al.10Peters et al. experimentally observed the impact process of rigid spheres in free fall and showed that suspensions with DST behavior exhibit viscous liquid-like behavior in which rigid spheres sink slowly without bouncing, whereas those with SJ behavior exhibit slight elastic behavior in which rigid spheres bounce slightly.14 Pradipto et al. simulated the impact process using the lattice Boltzmann method and reproduced bouncing behavior,19 which is consistent with Peters’ experiment. By analyzing the simulations, the authors state that the appearance of a dynamic jamming region is the mechanism of impact-induced solidification wherein the shear stress induced by the impact is small and the large normal stress is concentrated in a limited region. These results indicate that DST behavior determined by shear stress and impact-induced solidification dominated by normal stress are clearly distinguishable. The summary of rheological properties shown in Figure 5 suggests that the ϕ that maximizes shock absorption in the ball-drop tests is greater than the onset ϕ of the DST behavior and agrees with the onset ϕ of the SJ behavior. Based on the interpretation of Pradipto et al.,19 shock absorption is maximized for the specific particle fraction because of the following reasons. When a rigid sphere impacts a particle suspension in free fall, the response varies greatly depending on the rheological behavior of the suspension: in the CST and DST regions, the suspensions behave as a viscous fluid, and the impact is mitigated by viscous drag forces. This shock mitigation property increases with an increase in the viscosity and shear rate. In the suspensions with SJ behavior, impact-activated solidification occurs because of the collision of rigid spheres, and the suspensions momentarily behaves like a solid, generating a repulsive force against deformation. This slight elastic property reduces the impact mitigation properties of the suspensions. Thus, the balance between the viscous behavior of the DST behavior and elastic behavior of the SJ behavior results in the maximum shock absorbance of the suspension at the onset ϕ of the SJ behavior.Another point worth mentioning as a comparison with previous studies is the effect of the surface chemistry of the silica particles. Raghavan et al. reported that fumed silica suspensions formed a gel in PC, dimethyl carbonate, PEG dimethyl ether and PPG dimethyl ether, whereas they yielded a stable sol in EG, propylene glycol, PEG, and PPG.34 To explain the gelation behavior in PC, they concluded that hydrogen bonding is responsible for the dispersion of silica particles, despite the stabilization mechanism by electrostatic interactions in nonaqueous liquids proposed in previous studies.62,63 However, in our study, silica particles were stably dispersed in PC in an isolated form (Figure 11), and its stable concentrated suspension showed both DST and SJ behavior (Figures 2 and 3). This result is consistent with the stabilization mechanism by electrostatic interactions and appears to contradict that of Raghavan et al. This may be attributed to differences in the surface chemistry of silica caused by the different types of silica particles used. The surface of amorphous silica is composed of hydrophilic silanol groups (Si-OH) or hydrophobic siloxane groups (Si-O-Si) or with a mixture of both.64,65 Water molecules can be strongly physically adsorbed on the surface. Therefore, the surface chemistry of silica particles changes with the concentration and distribution of various types of silanol and siloxane groups, and they are sometimes bonded with water because of chemical reactions during the synthesis process. In addition, post-treatment, such as heat treatment in a vacuum or in air, or chemical etching in strong acids or bases, can also alter surface chemistry.65 Maranzano et al. addressed how surface silanol groups lead to short range electrostatic interactions that are shown to strongly influence the rheology of highly concentrated dispersions in a polar organic liquid.8 Bourrianne et al. investigated the effect of surface chemistry of fumed silica43 and confirmed that hydrophobic fumed silica formed a weak gel with a finite yield stress although hydrophilic fumed silica suspended in PPG exhibited DST behavior at high particle fraction. The yield stress results from long range interparticle interaction and masks shear thickening behavior. Others reported that the surface chemistry of silica affects the shear thickening properties of the concentrated particle suspensions.43,66,67ConclusionsConcentrated particle suspensions exhibit unique shear thickening behavior and have received considerable interest in the field of colloid and surface chemistry. Previous studies focused on their physical properties such as various rheological measurements such as DST, SJ, and impact-activated solidification, and the physical parameters of suspensions such as the effect of particle fraction and particle shape. Systematic studies based on the chemical viewpoints remain limited, particularly, studies on the effect of liquid polarity and hydrogen bonding capability. This study investigated the rheological behavior of the concentrated suspensions of silica microparticles using steady-state shear flow, pull-out tests, and ball-drop tests. The effect of liquids was comprehensively investigated using 14 organic liquids including polar, nonpolar, protic and aprotic liquids. Stability tests for dilute and concentrated suspensions demonstrated that the relative permittivity of liquids affects the stability of silica particles without surface modification and high relative permittivity values lead to good particle dispersion, consistent with the stabilization mechanism by electrostatic interaction in nonaqueous media.62,63 The steady-state shear experiment confirmed that high relative permittivity is preferential for the DST behavior. Furthermore, aprotic liquids exhibiting SJ behavior were, to the best of our knowledge, found for the first time in this study. A previous study by James et al. pointed out the importance of the hydrogen-bonding capacity of liquids.15 However, the liquids reported so far have been limited to protic liquids, which act as both hydrogen donors and hydrogen acceptors and are typical of liquids with hydrogen bonding capabilities. This study indicated the molecular interpretation of hydrogen bonding capacity for aprotic liquids and points to a possible extension of the liquid family of SJ suspensions. High relative permittivity and hydrogen bonding ability are not contradictory, and therefore good dispersion in high relative permittivity media does not deny the effect of hydrogen bonding ability for SJ behavior shock absorption on the ball-drop test was the maximum at the onset of the SJ behavior. This can be attributed to the balance between viscous behavior in DST behavior and elastic behavior in SJ behavior.Further study on the chemistry of highly concentrated particle suspensions is required in addition to the extensive research in physics. For example, molecular design to regulate frictional interaction between particles is important. Recently, chemically synthesized thermally responsive particles have been introduced and demonstrated rate- and temperature-dependent non-Newtonian rheology on concentrated particle suspensions.68–70 Understanding hydrogen bonding capacity based on the molecular structure and investing the effect of chemical bonding on the silica surface are promising approaches to achieve the precise control of rheological behavior through the molecular design of silica suspensions.ASSOCIATED CONTENTSupporting Information.The Supporting Information is available free of charge.Apparent viscosity plotted as a function of shear rate in a steady-state shear tests. List of suppliers and purity of organic liquids used in this study (PDF).Supplementary Video for rheological behavior of concentrated silica suspensions (MP4)AUTHOR INFORMATIONCorresponding AuthorSadaki Samitsu − National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanE-mail: SAMITSU.Sadaki@nims.go.jpAuthorsRyota Tamate − National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, JapanTakeshi Ueki − National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanAuthor ContributionsS.S.: Conceptualization, funding acquisition, investigation, methodology, validation, visualization, writing - original draft, and writing - review and editing. R.T.: Conceptualization, funding acquisition, investigation, methodology, validation, visualization, and writing - review and editing. T.U.: Conceptualization, funding acquisition, investigation, methodology, validation, visualization, and writing - review and editing.NotesThe authors declare no competing financial interest.AcknowledgementsThis study was financially supported by the acquisition, technology, and logistics agency (ATLA) of Japan. We thank Ms. Miwa Ohniwa, Ms. Misa Hazutani, Ms. Ayumi Murakami, and Ms. Mayumi Takenouchi for their experimental and instrumental support on the NIMS Molecules & Material Synthesis Platform.ABBREVIATIONSDMI, 1,3-dimethyl-2-imidazolidinone; CST, continuous shear thickening; DST, discontinuous shear thickening; EG, ethylene glycol; HD, n-hexadecane; PEG, poly(ethylene glycol); PPG, poly(propylene glycol); PC, propylene carbonate; SEM, scanning electron microscope; SJ, shear jamming; S-oil, silicone oil.References1. Barnes, H. A. Shear‐thickening (“dilatancy”) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids. J. Rheol. 1989, 33 (2), 329–366. 2. 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